I came on a weekday and joined the 4:00pm tour.
As you will leave the United States when entering the UN building that is why all visitors have to go through ID checks. The only exceptions were the groups or families where one adult would be checked and held responsible for everyone else. That person got the badge printed with their photo while the others were handed wrist bands. I was finished in five minutes, however, the guard recommended coming at least one hour early as lines can be unpredictable. Security screening X-ray and metal detectors) may be long depending on how well people followed the instructions.
After exiting security there was a small plaza with a few works of art including a gun with a twisted barrel called Non Violence. It was created by a friend of John Lennon after he was shot.
Inside the lobby, a statue of Nelson Mandela was close to the doors and seemed like he was greeting all of us.
The tour desk was to the rear of the main lobby. Once checked in, I was given a color coded sticker to ID my tour time and language (4:00pm had separate English and French tours).
Overall the tour lasted one hour and covered the UN history, initiatives and walked us by many of the exhibits and artwork arranged throughout first couple floors of the building.
We were fortunate that both the UN General Assembly and Security Council were live during our tour. We could walk through and observe the General Assembly (quite formal in operation) but the Security Council was a closed door meeting.
We got to enter another unused meeting room and sat at the back in very comfortable seats. Each one had earpieces for those attendees needing translations. For those sitting at the desks they also had their country names displayed and a voting pad.
An interesting factoid, the UN has over 100 interpreters working every session with at least 3 assigned per language.
The cafe, gift shop, credit union and gift shop were in the basement.
Another note, once the UN official hours are over all the member nation flags in front were lowered. Therefore if you really want those flags in your pictures then take your exterior photos before your tour and not after (tours 4pm or later).