Visiting St Tropez is for free, what costs expensive is going out and shopping.
If you're on a budget, the best you can do is stay at a town nearby, like Port Grimaud and go to St Tropez for the day.
To see lots of new rich, just take a sit between the yachts of the old port and Senequier (cafe), you won't miss one.
To eat, on a very tight budget, you can buy a sandwich and a drink at a little supermarket, Casino, near the port. Depending on what you order, some restaurants, like Joseph L'Escale, are not too expensive.
There are some affordable bars in front of la Place des Lices.
Going out at night, to clubs, it's expensive and, anyway, the porter won't let you in if he doesn't recognise you.
Visit the old town and galleries.
I visit the area quite often.