Why move the bases around overseas? Why not bring them home and defend our own borders for a change? I know this a revolutionary idea but it would conform to the original plan of operation called for by the Constitution.
That would be
Eritrea, imp. Has all of Ethopia's former beachfront property on the Red Sea, and their border dispute with Ethiopia is essentially resolved.
Doesn't seem to be too militantly Islamic, but I don't know if they're amenable to a US base there. Good location, though.