A few pointers:
* Paris districts (arrondissements) are numbered from 1-20, clockwise, starting in the center, so most interesting sights are located in districts 1-10
* On the right side of the river (rive droite): No. 1 contains the church of Notre Dame and the Louvre Museum. No. 8 has Champs Elysées and the Arc de Triomphe and also the "Triangle d'Or" with upscale designer shops. No. 9 has the large department stores (Galeries Lafayette, Printemps). No. 4 has the Marais quarter with Place des Vosges, the Picasso Museum, and many nice little shops. No. 16 is an upscale residential area.
* On the left side of the river (rive gauche): No. 7 has the Eiffel tower and the Hotel des Invalides.
* In terms of areas to stay in: I like the area around Place Vendome (No. 1). There are many luxury/upscale hotels clustered there (Bristol, Park Hyatt, Westin, ...) but also others. I also like the area around Place des Vosges (No. 4) - Hotel Pavillon de la Reine gets good feedback on FT, although I haven't staid there. If you are into luxury shopping, you could also choose one of the hotels in/close to the Triangle d'Or (Four Seasons George V, Peninsula, Plaza Athénée, Shangri-La), but I would say the general area is a bit less interesting and generally pricy (although very nice and quiet).
* Regarding the Latin Quarter: The overall area (districts No. 5/6) is certainly nice, but the Latin Quarter proper to me feels a bit like one big tourist trap. Not sure if I wanted to stay there.