Well, since nobody else wants to jump in here; I'll give a couple suggestions. (I have been to St Petersburg a couple times on cruise ship stops: however, I've never had a hotel room, flew out of or into, or looked for a luggage storage room there.)
1. Ask you tour guide for possible locations. My guess is there are hotels that for a small fee will store your luggage,
2. Ask someone at the closest tourist information centers: http://www.inyourpocket.com/russia/st-petersburg/arriving/touristinformation
3. If all else fails, you can store it at one of the train stations. Note: the Moskovskaya Metro Station and the Moskovsky Train Station are right next to each other.
a. All the train stations in St. Petersburg, have all the necessary facilities: luggage storage (24h), bank, ATM, post office, rent-a-car, business center (with internet access).
and apparently there is a bus that runs between the Moskovskaya Metro Station and the Pulkovo airport: To get to the Pulkovo I airport on your own, one should either take bus or mini-bus #39 from Moskovskaya Metro station or take a taxi. To get to the Pulkovo II airport on your own, you should take bus or mini-bus #13 from Moskovskaya Metro Station (about 15-25 minutes ride) or take a taxi.
b. Information on the two main train stations, see: http://www.expresstorussia.com/guide/petersburg-luggage_rooms.html
The hall inside the station has automatic cells (lockers) that cost around 30 roubles. They can be accessed 24 hours a day.
There are also two luggage rooms at the station. They are open 24 hours, but there is a 'technical' break from 2:00 to 5:00 AM. You need to present your douments to use the service. There are two kinds of luggage rooms:
Automatic cells, which cost about 35 roubles
Room with an assistant, which costs about 35 roubles for up to 50 kg and 70 roubles for more than 50 kg. You pay at pick up.
Turn right at the middle of the main hall of Moskovsky Station in front of the monument to Peter the Great.
There are two kinds of luggage rooms at the station:
Automatic cells, which cost about 30 rubles, and can be accessed 24 hours a day.
Room with an assistant, which costs about 30 roubles for up to 50 kg and 60 roubles for more than 50 kg.
Remember that luggage rooms have a few breaks and in spite of their 24 hour working day you may have problems getting your luggage when you want. However usually the employees notify you (usually with a sign on the window) when these breaks will be.