There is a Cuban town a mile or so away from the US base called Guantanamo. You wouldn't go there as a tourist, a few do to see the base from a far only.
Apologies not so exciting. It was an adventure however, as I became stranded there. I'd negotiated a car ride from the airport to a beautiful little place by the sea called Baracoa. But the hustler obviously didn't want to drive the whole way. So he chucked me out in Guantanamo by the side of the road - where Cubans congregate for a lift. I refused to pay the guy. The driver kicked off, as he'd driven me a third of the way. Everything is open in Cuba and the whole crowd got involved, like a jury they collectively decided what I should pay this hustler, I paid him, and was left standing in the dusty road praying for a car!