Birmingham airport is right next to the M42 which gives you quite good access to North and South sides of Brum. As an example, North of Birmingham is Sutton Coldfield (about 10 15 mins away) - the posh end of town according to Brummies (ie. we get out of the bath to take a piss). This has a pleasant town centre, and one of the largest parks in England. The Sutton Coldfield Observer has plenty of adverts for houses. About 10 miles further on is Lichfield; a well known cathedral town.
The airport itself is right next to Solihull of course, which is the second poshest part of Birmingham according to Suttonians. There should be plenty of housing there too.
A very brief guide I'm afraid, but I hope it helps.