There are plenty along Nevsky Prospekt and you can get a double room there for €50-€100 / night.
St. Petersburg has a lot of great hostels, which offer private rooms as well. Best of them we included in the section 3 Best Hostels in St. Petersburg, so have a look.
Rather than to book a cheap hotel, check private rooms in hostels first – and you might be surprised by the high standards of the latters.
As for the location, we recommend anywhere along Nevsky Prospekt for tourism and Vasilievsky Island if you want something not as busy and more authentic.
The local hotels are a bit overpriced, especially if you travel during the peak White Nights season, so better look for special offers in the Internet and book ahead.
We collected some of the best hotels for various budgets to make your travel easier.
Otherwise, renting an apartment for short-term is also a good idea in St. Petersburg, but be prepared that if you pay less than €50 / night you might end up in some Soviet style shack, unless you're into authentic experiences.
Compare hotel prices and find the best deal: