The worst time to be here is between end of Spring through early Fall, as far as tourist cost is concerned.
There is no one local market. There are many; different neighborhoods have local ones at different times. One you may find to your liking is the one near the Montparnasse train station; I can't for the life of me remember the exact Metro station name (not Montparnasse).
There are many many many cafes, many places where the locals hang. If you want to avoid the touristy areas, avoid St. Michel, Montparnasse, the Eiffel Tower, Notre Dame (which is close to St. Michel) and the Louvre. There are, however, various hidden streets where tourists hardly ever wander around, even at St. Michel and around the Eiffel Tower.
Hotels are expensive (depends on your point of view) no matter where, and what I recommend is that, if you're really traveling frugally, find a youth hostel (the "youth" is more of a traditional term now). You can find some of them and other hotels at ratestogo.com (if you're patient and you can sharpen your search skills, you can find some very good deals; four years ago I stayed at a three-star hotel in the 1er arrondissement for 40 Euros a night), but the deals are usually found "off-season" (meaning, Winter, as long as it's not around Christmas or New Year's Eve).
Where will you be traveling from?