Living with a host family is a good choice for a number of reasons. It facilitates language learning and gives an opportunity to learn Russian customs and traditions. Besides, one can get to know you what Russian hospitality really means: if a guest ever needs any help, the hosts will never say "no".
The host family for each student is selected by the university. Meals (breakfast, dinner) with the family are generally included into the program. When applying, it is recommended to give much information about your-self as possible, e.g. interests, favorite sports, special needs in diet, allergies, etc.
Dormitories probably lack the comfort of a hotel or a private apartment, but they do have their advantages. For example, it is easier to adapt to the new conditions there. Your neighbors are likely to help you whenever you need. Costs are considerably lower than those in any hotel.
A study/bedroom in the dormitory is often shared with a roommate. Bathroom and toilet facilities are usually shared as well.
If you want to be more independent, you are free to choose a hotel or a private apartment. The university will help in choosing the best one.
University is responsible for providing international students with accommodation. It can offer a private flat not far from the University with all facilities.
In general, hotel prices in Russia, excluding Moscow and St. Petersburg, are relatively low. Hotel rooms are inexpensive; the cost does not exceed $85 per day. As a rule, one can obtain a good quality room (shower, toilet, telephone, TV) for approximately $40 per night. Deluxe rooms contain double beds. Most hotels have eating facilities with different types of kitchens, bars, and saunas.