St Germain is pretty cheap, both in terms of accommodation and food/drink - think lots of students, young professionals, Latin quarter & muti-cultural people.. the hip and trendy, rather than flash.
Pick up an offer on a boutique hotel and as you're only a tube ride away from anything anyway, it doesn't really matter where you're based. I'd avoid anywhere near the La Grande Arche de la Défense (although the prices will seem appealing), tis a bit boring and cut off come late night, as it's more a business quarter.
Sacré-Coeur has been mentioned, fantastic, just watch for pick pockets.
Louvre and Pompidou are great and you can spend a day in there if it is rainy.
Père-Lachaise cemetery, Jim Morrison's and many other famous graves... odd choice I know, but it's pleasant.
For a little known view of the city, there's a cocktail bar and restaurant at the top of the
Montparnasse Tower which overlooks the Eiffel Tower.
Top tip. Every restaurant will have a set menu on that day, it will be very reasonable & house wine is always good, the French wouldn't stand for crap, and it's much much cheaper than beer. Grab a copy of The Rough Guide from your library too, they've always been handy when I've been travelling, if a little snooty of the cheaper places.
