Agree with the advice in regards to parking, the United Methodist church lot works out well. As far as hotels go, there are several "budget"-type hotels back in Alexander City. They're about 35-40 mins away back west on Highway 280, not quite as far as Montgomery (or B'ham for that matter). There's an American Inn (not a chain & slightly cheaper) as well as a Days Inn, Quality Inn, & Super 8 (all seemingly around $99/night) and a Hampton Inn (nicer but more expensive). You might be able to find a good rate through Priceline, Expedia, Trivago, etc. provided there are still rooms available.
Another option I saw on Google Maps was a place called Creekside Lodge (click here) which is right on Lake Martin in Dadeville. Only about 25-30 mins to Auburn but unfortunately they have a 2 night minimum stay on Auburn game-day weekends 😠I was lucky enough to stay at a friend-of-a-friend's cabin on Lake Martin when we went down to see the last game that Harsin coached aka Auburn vs. Arkansas. Wish it was my place, I'd offer it up to you as a fellow Tigers fan. Only about 25 mins from Auburn and the sunrise views there were pretty nice!