Sheregesh is a medium sized miners settlement, so it's not really a great party place, unless you're lucky enough to get together with some locals to experience a few-day long vodka marathon (which may end up badly, though). There's a number of snowboard competitions taking place at the mountain every year, during which there's a good chance to hang out with some snowboarders.
There are several cafes and restaurants which are located mostly in hotels. More cafes can be found at the bottom of the mountain, where you can have a meal for 200-400 R ($6-$12).
The nearest hotel to the mountain is "Gubernskaya" hotel. The rooms cost $100 / night (for a double) over there. The other expensive option is "Elena" hotel for the same price. There are many small budget hotels around the mountain, where you can find a room for $50 per night. Rooms are avilable even during the high season, so is not necessary to book ahead. Most of Russian tourists prefer to rent apartments due to relatively low prices. Prices starts at 600 R ($23) per apartment (up to 6 persons). To find a landlord, go to Dzerjinskogo ulitsa (the central street of the Sheregesh settlement) and ask for available rent ("arenda kvartiry").
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