Officially it starts on Wed and ends on Sunday, a lot of us go up earlier. Actually some of us take the whole week. It's about a 10 hour drive down there and then another 10 back, so I like to really stay once I'm there. Fontana is currently booked as many of us book before we leave, but you can usually get in as people find they need to cancel
There are alternate places to stay listed on the site. The first year we stayed at the Microtel, which is about a 20ish minute fun drive to get to things. It's not that far, but you do miss out on a lot of the evening fun.
If you haven't looked yet here's the site http://www.minisonthedragon.com/lodging.php
It is a really fun time. You can get to meet a ton of MINI people, get mods done on your MINI, have a blast driving and enjoy some beautiful scenery.