Location! Location! Location!
The best areas to stay in St.Petersburg is a Central District, any place close to: St. Isaak Cathedral Kazan's Cathedral, Russian Museum, Palace Square, Moyka River, Griboedova Canal, Nevsky Prospect from Admiralty to Gostiny Dvor.
Booking a small hotel or an apartment ALWAYS MAKE SURE that your accommodation have a lift! Some old buildings don't have any lifts and this will cause great inconvenience.
Vasilyevsky Island is a great place but remember of our drawbridges open during the summer months. Be on your side of the river before your bridge will be open!