Montgomery, Al is putting together a package to try and get it moved here when the current deal with Hoover is up.
River Walk is an awesome venue and the Sun Belt is doing their tournament there this year. There is a parking garage right next to the stadium as well as additional parking not too far past right field.
I'd also mention Hank Aaron Stadium in Mobile. It's not as big as Hoover but there isn't a bad seat in the house. Plus there is more to do in Mobile than in Birmingham.