something to think about.
if you are gong to cross boarders you may want to think about leaving from Paris if you fly into London. You can buy OPEN JAW tickets and not have to deal with back tracking. But its up to you how you want to travel.
Theres noting wrong with doing what you want, but it will save you the time and $$ backtracking.
with regards to where to stay, i use this site and travel books.
you can check out travel books too. They have info such as where to stay and what to do in Paris. If you have a desktop you can look at the top of the page for each destination and look at the "things to do and see". Also, note that some travel books will have "Paris in 2 days" so you can get an idea on what you want to see. But i would do some research on Paris and determine what interests you. Everyone will have different likes and not.
with regards to where in Paris, i try to find someplace "central" to where i will be venturing out everyday. Again, travel books have hints. One thing you will want to do in both places is to find a place near a Tube/Metro stop. You will use them alot in both places. There are buses too, but i found that using the Tube/Metro easier to figure out and faster since they run underground (most of the time) and not have to deal with traffic issues up top.
If you use the booking.com site always check directly with the hotel before reserving. Often that website shows inflated prices and claims hotels are full when in fact they are not. Not the nicest neighbourhood but for an overnight with arrival & departure from Gare du Nord I would stay near that station.