I want to stay someplace close to the city center, but am on a tight budget....any tips?
I've stayed at the Hostel in Caulaincourt Square http://www.caulaincourt.com/ a few times. It's in a beautiful part of the city - up near Montmartre. I could happily spend more weeks in that area just lazing in cafes and buying food from the markets.
The hostel can be fun, depending entirely on the people staying there. I've had one very good experience there - impromptu parties in the foyer - and one fairly restrained experience where there were simply no remotely talkative people anywhere.
It's practical, pretty cheap, and fairly close to the centre of Paris. about 8 years ago
To find the cheapest stuff I always use hostelworld.com and hostelbookers.com.
I stayed about 10mins by underground from the city center, it was something like 20euros per night and it turned out to be a private room with ensuite. This was in the middle of peak season. almost 8 years ago