Best way to check would be your local recruitment center.
A lot depends probably on the job you enlist for. People trying for flighttraining will for example have to enlist for a longer period than someone enlisting as a cook or security guard.
soldiers can be stationed anywhere in the world. I think that for non-com ranks there is a policy to station them close to their hometown if possible (not sure, think I read it somewhere), officers are always in short supply and will typically get assignments all over the place.
If you do not want that, join the National Guard instead, they stay within their own state unless federalised (usually in times of national crisis like war or major natural disaster) or for shorter duration deployment exercises.
The USAF has permanent bases in the UK, Japan, Diego Garcia (Indian Ocean island hellhole/paradise), Germany and Turkey (maybe elsewhere as well).
I wish I were flying