Most (if not all) of the people who stay at the Capstone Inn have reserved (and have to pay for) every weekend that there is a home game. We have been lucky enough to get a room there once on a football weekend. The next closest would be the Hampton Inn on Harper Lee Drive, but it is usually booked up as well by people who have reserved it for the whole season.
Our favorite place to stay is the Hilton Garden Inn out on Hollywood near Courtney Drive. There is also a Marriott on Courtney almost next door to the Hilton Garden that is nice.
At the LSU game a couple of years ago, we decided to go at the last minute and could not find a room anywhere. I went on e-bay and bought a room at the LaQuinta off of McFarland. It was okay, but it would not be my first choice. It was a room that an LSU alum had bought as part of a travel package for LSU alumni. He just called the hotel and had the reservation put in my name and I paid him by paypal on ebay. Worked great.
If you really want to stay at the Capstone Inn, you could call them on Friday afternoon to see if they have had a cancellation. They do not have a wait list. Just remember, any room in Tuscaloosa on football weekends falls under special guidelines and you cannot cancel once you book. Even the LaQuinta has a two night minimum and was $250 per night. There are no bargains to be had on game weekends....except maybe the MoonWinx or the Olde English Inn ;-)