Day 1 – a panoramic city tour with visits to Peter-and-Paul fortress, St. Isaac’s cathedral and the Church-on-Spilt Blood (approx. 6 hrs.)
Day 3 – a day at the Hermitage – a tour of the museum and the two Gold Rooms (approx. 5 hrs.)
Of course, everything depends on your interests, some places could be skipped, others visited instead. There's a couple more summer palaces outside the city - in Oranienbaum and Gatchina, there are more palaces within the city limits - the Engineers' (Michael's) castle, the Marble palace, etc.