Its St. PetersbUrg
My home city and very beautiful city and unfortunately 4 days won't be enough to see even a fraction of it.
Firstly I would recommend visiting "Petergof". It's located just outside of the city on the coast of Gulf of Finland. If weather is nice, its a great place to spend whole day. Loads of old buildings to see along with gorgeous parks and loads of fountains. You can get there by car/coach or on a boat from city.
There are loads of museums and art galleries. Hermitage is world famous and one of the beautiful museums around. And its massive. I think they said if you want to stop at each picture or other thing for 5 secs, you will need like 2 weeks to look at it all
Since city is build on river Neva, there are hundreds of bridges there. At night they open large bridges so big ships can pass. It's quite spectacular and very popular thing to watch. So that's something to do at night, as well as loads of restaurants to eat. There are few very nice roof top restaurants that have amazing views.
City center is very nice, especially at night when all lights are on and there are plenty of things to see close buy as well. One of them is "Spas Na Krovi" (The Church of the Savior on Spilled Blood). Gorgeous place.
River boat trips are very good as well, so i would recommend that as well.
What dates are you going? As I'm going there in September as well for 2 weeks.