There 3 major mobile Internet providers in Russia: MTS, Beeline and Tele2.
Beeline and Tele2 are available at the Pulkovo airport plaza at the ground floor. Ask for an unlimited Internet access (costs ~350 RUB for two weeks). You will need your passport to get a sim card.
There are lots of great places to visit and taste. Check the nearest with Google maps. The most unusual are mentioned below.
Sever-Metropol ("СЕВЕР" in Russian) is a local cake-shop. Nice place to have a cup of tee or coffee and taste some local cakes and sweeties.
Caviar bar, shop and enogastronomic space with a wide selection of alcohol traditionally combined with black caviar. Booking in advance is advised.
Learn and taste different Russian Vodkas