You don't need to book a tour of St. Petersburg to really see the city. It's one of the most beautiful places on this planet. When the boat docks, you can take off on your own, get a map, it's an easy city to walk around. The Amber Room is in Tsarkoye Selo, that may be a bit out of your way. However, the Hermitage Museum is right in the center of the city, in a magnificent square.
The most amazing thing about St. Petersburg is that it was almost totally destroyed by the 900 days siege of the Germans in WW II. It has been restored to the last gold leaf. Hats off to the Russian for preserving the beauty of their heritage.
I'm sure you could take some form of public transportation to go to Peterhof, the tzars palace by the Baltic. Spectacular !!!
Be ready for long lines at the museums, but worth every minute spent.
Have fun and take pictures.