T.H.
Je t'aime Paris! I have only had the opportunity to go twice, but long to return. We stayed in a little B&B on Rue Cler (I am awaiting a return call from my husband to confirm the name of it). Rue Cler is a pedestrian only street walking distance to the Eiffel Tower with little shops and restaraunts all along it (one for just cheese, one with fresh breads, one specializes in wine, etc). It is adorable!
As far as seeing the city, you can take an inexpensive tour by boat. There are several compaines, but I suggest
Bateaux Mouches. It is Paris' most famous boat tour company and is easily recognizable by its enormous decks and bright orange seats. Bateaux Mouches has a fleet of 14 boats, some of which offer lunch and dinner service.
There is all the info you could ever wnat on this website:
http://goparis.about.com/od/sightsattractions/a/Paris_Boa...
However, my favorite way to see the city is on bike. Bike About Tours give several affordable tours daily and the trip includes history of the city and a snack along the way. Paris is fairly flat, so riding a bike around is easy and gives you such a better perspective than just taking the metro everywhere. On the metro you are underground so much, I never really understood where things were in relation to each other until I took the bike tour.
As far as sites - visit St Chappelle Cathedral. It has the most original stained glass in a church in all of western Europe (so much was destroyed in the wars) and is stunning. We loved spending some quiet time in Le Jardins de Tuileries. And stay up late and visit the Eiffel Tower after dark. The millenial lights go off for 10 minutes on the top of each hour after the sun goes down. It is breath taking and you can enjoy a crepe with Nutella while sitting in the park watching the lights. You can't go wrong in Paris!