Assuming it does happen, I think a Communist Cuba would be a way more open and pluralistic society than most Communist nations, and likely with more independence from the USSR: something more like OTL Yugoslavia or Sri Lanka.
I know Cubans have a somewhat ambivalent attitude toward their status as the western hemisphere's foremost sin-bin, but still: you don't likely go from a bastion of cosmopolitan excess to a puritan stalinist dystopia just because you had a revolution. They'd likely keep up the debauchery tourism, not to mention the free-wheeling music scene, which keeps a multiplicity of cultural tendencies coming in.
And they'd need to maintain good relations with the US(not least for the tourism), which means resisting any Soviet attempts to use their country as an aircraft carrier or missile pad.