What's the military value of Guantanamo Bay?

I get the value in having a naval base in the Caribbean back when ships were coal-fired and ranges were a lot shorter, and the RN still posed a significant threat to the USN in the hemisphere, but what value does the base give now? Especially now that the cold war is over and Cuba's no threat, any operations from the base seem like they would be easier to run out of Florida or PR, which are both close by. Is there any reason for holding on to gitmo besides it's a convenient offshore prison and it pisses off Cuba?