The main post office (Glavpochtamt), Russia's first, opened in 1714 and is a couple of blocks from St. Isaac's Square.  A grand building serves as the postal headquarters on Pochtamtskaya ul. and has different service counters on all sides. From here you can send packages home (don't wrap them as they will need to be inspected at the counter). There is a central island which contains a stationery and souvenir shop and the section where foreigners can complete registration. Of course you can also buy stamps in any city's 400 sub post offices - just look for the blue post sign. Letters can be posted in the light-blue post boxes around the city. The Central Post Office has a cash machine.

Stamps need to be dated after 1998 and they should not be USSR stamps otherwise your mail is even more likely than usual to go nowhere. (Some kiosks in the city centre tell international visitors that they have to buy a 10Rbl stamp and a 6Rbl stamp for one postcard - the 6Rbl is an USSR stamp).