You could check out if the Mariinsky Theater has something interesting on while you are there :
https://www.mariinsky.ru/en/
I was not very impressed in general with the restaurants I tried and I don't remember most of them.
I enjoyed my visit to this restaurant though:
http://en.orient-express.spb.ru
Mainly because of the decor but as far as I remember the food was quite good as well.
And remember to go for a late evening walk to enjoy the white nights....