I had been living in S-Petersberg (SPb, an official abbreviation) for seven years. Here are some considerations about what you shouldn't miss there
-The Hermitage (Winter Palace). It is not only a large collection of different arts, but also the place where Russian emperors (tsars) used to live.
-Peter and Paul fortress.
-Isaakij Cathedral. Beautiful cathedral and the highest building in the city. You can observe the whole city from its top.
-Petergof(Petrodvorets). Former summer palace of tsar, nice parks with spectacular fountains. You should take a bus or train from Baltijskij railway station, the trip takes about 1 hour.
-Boat trip on rivers and channels of S-Petersburg. There are little boats waiting for tourists at the crossings of Moika river and Griboedov channel with Nevski prospect. It is worth to see the city from water.
-Opening the bridges. In summer time the bridges over Neva river are opened during the night to let big ships go up the river. And there is almost no night in SPb in summer, 'white nights' as we call them.
Those are the main sights to my opinion.If you had seen them I would say you saw the city.
If you have time for walking, I would recommend to walk along the whole Nevski prospectand in Petrogradski region (Petrogradskaia storona). Walking around Sennaya ploshchad (Hay square) would take you in Dostoevski's novels (if you like it, of course:).
Visit Vassily's Island and look at two famous marmor columns.
Fondest memory: The Neva River is the city's greatest beauty and the greatest danger at the same time. Water level in the river often rises for some meters. That day I took this picture, Neva was quiet and covered with ice.
Favorite thing: Not everyone in St.Petersburg is Russian Orthodox! Here is a picture of a beautiful mosque we saw while walking around.