The trip to the city is just awesome.You will really never forget this place once you come back to home.The best time to visit Russia according to me is summers because the temperature is just perfect and you would love to take long walks on the road specially during evenings. St.Petersburg witness white nights during the months of May-June, so it is a new experience in it too. Its a very diverse city and according to your preferences,you can plan out your trip, if you are a party-person, just go out on some specific streets and there are so many clubs and pubs from low to medium range there. And if you want to understand about culture and history of the country,there are literally hundreds of museums,and museums like hermitage-winter palace are a must.Also dont miss the opening of the bridge during the night, its a spectacular view.There are a lot of concerts going on in the city and if you are lucky like me, you might also get a chance to attend linkin park live concert!!.Since i was on this trip for a social internship through AIESEC, I did not had to pay for my stay (hostel,etc.) and sometimes food.
I think 15 days trip to Russia is a good time and depending on your travel type,you can choose various cities.But I think it would be better to get in touch with a russian or go for a organized tour because there is a lot of english language problem in this country. Most of the people don't even understand basic english words.