The hotel is very convenient to the airport -- at least in the summer months you could actually take a long walk to get to the terminal if you want, but otherwise you need the hotel shuttle or a taxi (despite the fact that you can see the airport, there's no very easy way to get there). I've never done the walk, but I've been told you could actually walk there if you wanted to.
If you really want somewhere to stay before you fly out I'd try the Novotel (which is actually connected to the terminal).
However, I found the Hilton accommodations disappointing. The rooms could really use remodeling!
Instead, I've chosen to stay at the Marriott in city center Birmingham when I'm in town.