Hotels or Hostels?
If normally you would stay at a ‘best western’ or ‘days inn’ places along those lines, then i would suggest a hostel.
that is not to “don’t” look into hotels in europe, but hostels usually an all around better option. just be open to some different options ( also some hostels will call themselves hotels to sound familiar to americans,)
hostels are usually a friendly environment, cheap, and you can meet other people that are travelers.
here are 2 sites that might help
http://www.hostelworld.com/
http://www.hostels.com/
as far as neighborhoods, here is a link that shows the districts that paris is divided into
http://www.parisnet.com/parismap.html
you can look for attractions you are interested in and hostels/hotels that are near them. that site also expains what each district is known for (i.e. clubs, museums, churches, restaurants etc).
for amsterdam you will best off renting bikes to get around town, and for paris buy a week long unlimited metro pass (or however long you are going to be there).
LASTLY!
amsterdam might have something like this too (idk), but if you are going to go to a lot of museums in paris, you can get a museum pass. Over 60 museums and monuments in Paris and on the outskirts of Paris can be visited for free with the Paris Museum Pass.
http://www.parisnet.com/parismuseumpass.html