To get your bearings: 

 

Going up towers/viewpoints:

1)   Fernsehturm (TV tower) on Alexanderplatz
One of world’s tallest towers with still largely GDR aesthetic. Restaurant as well as viewing platform (which revolves).  Open till midnight.  (Transit: Alexanderplatz - U2, U5, U8, S-Bahn, trams). tv-turm.de

2)   Panoramapunkt in Kollhoff Tower, at  Potsdamer Platz 1
Fastest lift in Europe. Open till 8pm. Cheaper than TV tower. (Transit: Potsdamer Platz - U2, S-Bahn, 200 bus). panoramapunkt.de

3)   Dome of Reichstag building. (stunning architecture by Norman Foster, and wonderful views) Open till midnight; last entry 10pm. No charge to visit but you have to reserve (and produce ID) , it is also possible to pre-book the restaurant on the roof (Dachrestaurant)  http://www.bundestag.de/htdocs_e/visi.... (Transit: Bundestag - U55, 100 bus).

4)   Siegessäule (Victory Column) in Tiergarten park   Transit: Hansaplatz - U9, Bellevue - S-Bahn, 100 bus).

From all these viewpoints you look down on the city and see how quickly it is changing. This is especially clear if you look at the photos displayed in the TV tower and at Panoramapunkt (as you come out of the lift).

Boat trips on river and canals:

With a trip on the River Spree and on the canals of Berlin you get a view of the city you can’t get any other way. The three-hour trip is circular and you'll be on waterways that were off-limits while the Berlin Wall was in existence. Various companies do the trips, eg from near Charlottenburg Palace and near the cathedral.

The one-hour boat trip is also interesting, but you remain in central Berlin, going past Reichstag and other (modern) goverment buildings, as well as Museumsinsel and Nikolaiviertel.
It is also possible to walk along the banks of the rivers and canals in many parts of the city.

 

Scenic rides: 

Bus 100, 200, M29:
The famous bus routes are the 100 and 200 routes between Alexanderplatz and Zoologischer Garten. They both run along Unter den Linden but whereas the 100 goes past the Reichstag building and Schloss Bellevue (and Tiergarten park), the 200 goes via Potsdamer Platz and the Kulturforum. Another interesting route is the M29 which starts in Kreuzberg. http://www.budgettravel.com/feature/a...

Berlin buses are double-deckers like in Britain so views are especially good on the top deck. You can obtain a map of the city with main bus routes of interest to tourists from BVG offices

 

S-Bahn from Zoo to Alexanderplatz:
As the Stadtbahn system runs mainly above ground you have fabulous views en route including of the zoo and Tiergarten park and the new  government district and Reichstag. Third station is in the new Central Station (Hauptbahnhof, former Lehrter  Bahnhof) which opened in May 2006, and is where S-Bahn and main lines cross on different levels. This is Berlin’s first central station: in the past like London and Paris it depended on which direction you were heading which mainline station you went to. After Hauptbahnhof the train runs alongside the red-brick Charité hospital complex (left-hand side) which is in Mitte district (part of  East Berlin at the time of the Wall).
During the division of Germany the S-Bahn system was run by East Berlin authorities and was generally boycotted by West Berliners, especially after the building of the Berlin Wall.

However it was used as a means to cross into East Berlin to visit. Friedrichstrasse was the station where all passport-holders could move from East to West Berlin (with strict controls).  The building where the controls were carried out can still be seen from the train and now houses a free exhibition about that period "Border experiences. Everyday life in a divided Germany" http://www.hdg.de/fileadmin/static/en...  You can also see the gilded dome of Neue Synagogue on Oranienburgerstrasse. Soon after leaving Friedrichsstrasse the train goes between the museum buildings on  Museumsinsel before stopping at Hackescher Markt and then continuing to Alexanderplatz station.

Interesting areas to visit: 

Scheunenviertel
Hackescher Markt, the station before Alexanderplatz is the stop to explore Hackescher Höfe the renovated complex of courtyards with shops, housing and restaurants) and the old Jewish district, the Scheunenviertel. Mainly low-level older buildings (Sophienstrasse is particularly attractive) and incredibly quiet for the centre of a big city. Jewish school and site of old Jewish cemetery (now a memorial garden) on Grosse Hamburgerstrasse.

For older kids, and adults Centrum Judaicum in the Neue Synagoge is well worth a visit as you learn about Berlin’s Jewish community and see the effects of Nazism in situ. Don't be put off by police guard in front: sadly all Jewish centres in Berlin have these (because of threats). Nearby, towards Friedrichstrasse, is Tacheles, alternative arts centre (looks like a semi-ruin) which featured in the film  “Goodbye Lenin”.  

Alexanderplatz
This was the social centre of East Berlin and still has various examples of “real-socialist” architecture although the area is still being redeveloped, more recently including the Alexa shopping centre. Its most famous sights date from GDR times, the Fernsehturm/TV tower (viewpoint mentioned above) and the Weltzeituhr (clock showing the time in different cities worldwide) which was a popular meeting-point.

Potsdamer Platz area
This is a modern development on what was the boundary between East and West Berlin. Building work is still going on esp. in Leipziger Platz and it is fascinating to see a whole new quarter as it develops. A few slabs of the Wall are still in situ and in the pavement and on the road you can see a line of stones which shows where the Wall ran.
Potsdamer Arkaden atrium is very attractive, good for shopping as it’s not too big and has a good mix, with designer names discounted, Zara etc plus non-clothes incl. a mid-sized branch of Hugendubel bookshop (which has books in English including a selection of books about Berlin in English, not just the usual guidebooks.). One shop to look out for specially is Ampelmann shop (in the basement) with souvenirs of East Germany's "green man" who is fatter than other versions and wears a hat. Most pedestrian lights in the eastern part of the city (Mitte eastwards) still have lights with this figure and occasionally lights in the western part of the city do too.
For food: good variety of eateries in the Arkaden and attractive café terraces across the road,  “under the tent”  in the Sony Center . This is worth a visit in any case because it is very impressive architecturally. In the vicinity also: IMAX cinema, Film Museum (history of German cinema) and Panoramapunkt viewpoint (see “Viewpoints” above).
 
If you walk from Potsdamer Platz towards the Reichstag building (e.g. to visit the viewpoint in the dome) you follow more or less the line of the Wall and come to the Holocaust Memorial, known also as the Memorial to the murdered Jews of Europe There is open access to the Field of Stelae which consists of  2711 grey slabs of varying heights laid in rows. Below the memorial (access from opposite side of memorial) there is an underground visitors’ centre which tells the story of some of the victims of the Holocaust. 

 

Museums and other visits:

To find out information about Berlin's myriad museums: http://www.berlin.de/international/mu... and http://www.museumsportal-berlin.de/en...  In many museums children (up to 18) get free entry.

 Jewel in the crown of the Berlin museums is the Pergamon Museum on Museum Island (Museumsinsel) with Ishtar Gate from Babylon, Pergamon Altar, Market Gate of Miletus and lots of other antiquities.   

The Egyptian collection which includes the head of Nefertiti amongst its treasures is now housed in the renovated Neues Museum,also on Museum Island. http://www.neues-museum.de/  The museum also houses the Museum of Prehistory and Early History which transferred from Charlottenburg.
 

Märkisches Museum has traditional display on history of Berlin (a lot of labels and panels are in English as well as German ). It is situated in what was East Berlin so interesting stuff on GDR history. The whole family enjoyed our visit there a lot. 
 

“Story of Berlin” shows Berlin history in a much more dynamic way with lots of multimedia presentations, but it can be confusing. It is possible to combine with a visit to the nuclear shelter underneath the building which would be an interesting (if unnerving) visit for older children. www.story-of-berlin.de
 

Deutsches Technikmuseum Berlin (Technical Museum) Very large, with science center also. SPECTRUM- Science Center located in separate building near the museum is highly recommended for families with children. Instead of boring museum exposition there are a lot of different experiments children can do themselves. www.dtmb.de
 

Checkpoint Charlie Museum (Mauer-Museum Haus am Checkpoint Charlie) is the more famous of the two museums relating to the Berlin Wall. Given its foundation as a private initiative soon after the Wall went up at the height of the Cold War its presentation is inevitably propagandistic and different from the sober factual presentation at the government-run Berliner-Mauer-Dokumentationszentrum on Bernauerstrasse.  Displays at Checkpoint Charlie include many objects relating to successful escapes and will probably have a more immediate appeal to kids than the documentation centre. Incidentally the hut at the crossing point is a reproduction; original in the Alliertenmuseum. www.mauermuseum.de  
Website for Bernauerstrasse :  berliner-mauer-dokumentationszentrum.de 

To understand why some people were so desperate to leave the GDR that they would risk their lives, you can visit two Stasi sites. The Stasi documentation centre at  Zimmerstarasse 90/91 very near Checkpoint Charlie shows the extent to which the Stasi monitored daily life in the German Democratic Republic. Examples of spying equipment include a watering-can with camera used to spy on mourners at a funeral. Here you can also see the attempts made to destroy the evidence of Stasi activity in the autumn of 1989.  http://www.bstu.bund.de

Even more oppressive is a visit to the massive Stasi-Zentrale at Normannenstrasse (Transit: Magdalenenstrasse - U5). Stasi trophies, spying equipment and more, plus the chance to walk through the rooms of Erich Mielke the Stasi boss. Info on the walls is only in German; explanatory notes in English can be borrowed at desk. www.stasimuseum.de
For a glimpse at everyday life in the GDR, the interactive DDR_Museum, is excellent. On Spreepromenade near Liebknechtbrücke (near Berlin cathedral) 

 

West of the city centre there is:

Charlottenburg Palace.
Built by the Elector Friedrich III and extended and by his successors from Friedrich  the Great to the last Kaiser. Badly damaged in the Second World War but restored to its former glory as a priority soon after. Beautiful gardens too. www.spsg.de


Olympic Stadium, further out but on U and S-Bahn routes. 
Built for the 1936 Olympics; remodelled for 2006 World Cup. Home of Hertha BSC football club. Guided tours or self-guiding (audioguides available). www.olympiastadion-berlin.de   Opening times depend on events organised in the stadium (matches, concerts etc)
  

Animals:

Zoologischer Garten (Berlin Zoo) is very central, near the Ku-damm.
Germany’s first zoo, opened in 1844, has the only giant panda in German zoos..
Aquarium (within the zoo complex but has separate street entrance also). Dates from 1913; has over 4000 specimens including crocodiles and insects as well as aquatic species.
Sealife Centre Berlin is next to Radisson SAS hotel in the Dom-aquaree complex near the cathedral. As other Sea life centres, concentrating on local aquatic environment. Special feature is the Aquadom lift.

 

Outside the centre:

Tierpark , Berlin’s second zoo was set up in 1955 in Friedrichsfelde in eastern Berlin (U-Bahn line 5 to  “Tierpark”). Very extensive grounds(160 hectares to the Zoo’s 35!)
Domäne Dahlem in south western Berlin is an old manor which is still a working organic farm (farm shop) ; also handicrafts centre.  www.domaene-dahlem.de (includes English version).