The hotels usually DO sell out for football weekends well in advance. Some of the hotels require two-night stays. Remember that UVA draws from all over Virginia and it's a big enough state that some people are coming a long way—the Tennessee state line in Bristol, for example, is around 380 miles from my house via the I-66->I-81 route. If you want to book a hotel, make the reservation as soon as the game date is announced. The best thing to do is to book for both Friday and Saturday nights and then adjust it later once the kickoff time is announced. That way you're covered if it's a noon game and you just want to stay Friday night and you're also covered if it turns out to be a night game and you just want to stay Saturday.
Tickets aren't hard to get, although most games usually either sell out or come close. As with any sporting event, all you have to do is walk down Alderman Road near the stadium and listen for scalpers.
