Personally, I can’t think of anything more thrilling than flying — or falling. If you’ve already tried parachuting or rope jumping, you know what I mean; if not, your first time will surely become an unforgettable experience — and a great adventure to tell your grandchildren about.
There are many organizations where you can try parachuting; the average price for a jump is from 3000−4000 rubles if you jump alone or about 6000−7000 with an instructor. Most offer additional services like making a selfie in the sky or video-recording your jump. Note that before jumping, you will have to go through a briefing and basic training, so plan your time accordingly.
Rope jumping is cheaper, but thrilling no less. The price of one jump can be from 500 rubles and higher; also, there are many places to jump from within the city, so you won’t have to leave it. Those are mostly abandoned plants or heat power stations; the height you jump from can be up to 88 meters.
As for choosing where to go — there are several organizations in and around Saint Petersburg that provide these kinds of fun. Note that prices differ from place to place — sometimes, you can save a lot by spending a little more time on the road.
Another good option for spending your free day in an adventurous manner may be going out of the city. If you’re not a fan of hiking, you can always rent means of transportation, and I don’t mean some car. Riding a quad-bike, a skidoo and especially a horse will surely make you feel tall in the saddle. Don’t forget to bring some snacks and a thermos — everything tastes twice as good when you’re resting outdoors!
If you’re thinking of resting for a couple of days, you should consider staying at a tourist base — most of these offer both activities and accommodation, not to mention catering and traditional things like banya that you should definitely try out (for further information, check the links below).
Regrettably, most organizations don’t have an English version for their websites, so consulting your Russian co-students might be a great idea. In the end, any activities are best done in company.
If you don’t have all day, there are some other options that don’t require much time.
Rock climbing has been becoming more and more popular in Russia, so there are many places to do it even in winter — there are several big climbing gyms in Saint Petersburg and new ones are being opened from time to time. As for the sport itself, it’s both great fun and a way to stay fit, so it’s surely worth a try — who knows, it may well become something you’ll start doing regularly.
Among other activities that combine both sport and leisure are skating and roller skating. Though not something "extreme", it’s fun and a really great way to change your mood and do something different. Rollerdromes and indoor skating rinks can be found in almost every district of the city, and with the coming of winter, many outdoor skating rinks will be opened. Visiting public outdoor skating rinks was somewhat a tradition in the Soviet Union, which is still definitely worth trying.
To sum up, if you need a distraction, there’s much to do in Saint Petersburg — we’ve only mentioned several of the many options you have, and any advice is, obviously, subjective. Still, trying them out may be a good start — eventually, anyone can find something to his liking, and doing something new is the best way to gain experience. As it may be hard to find more detailed information in English, here are some links in Russian that might be of use:
https://kudago.com/spb/recreation/
http://katalogturbaz.ru/russia/leningradskaja-oblast