While we mentioned Cuba, Fidel Castro actually wanted a close relationship with US right after he took power. He even flew to US seeking to meet with Eisenhower. However, Eisenhower decided a game of golf was more important than meeting him, and started hosting right wing Cuban exiles in meetings. That forced Castro to fall back to Soviet Union for support, becoming one of the major blunders of US diplomatic history.
Castro did want a closer relationships. But he always wanted to be a major worldwide player. Remember Castro's government tried to destabilise several governments just like the US did. The Congo and Venezuela for example. Where Castro tried to bring about a revolution of the democratically elected government of Venezuela. Even Che in Boliva.
It is a shame that the US embargo existed and ruined the relationship with Cuba.
Personally I never saw Cuba and the US being very close under Castro. Especially when Che was alive. Che didn't even like the relationship with the soviet union.
I think Castro played Chavez beautifully. He appealled to Chavez's emotional side. My dad worked under chavez for a period of time. He said Chavez saw himself as a liberator. And Castro made him think he was. And Chavez felt he had a mentor in Castro a fellow liberator. And Castro convinced Chavez to give Cuba a lot of help and rights that some Venezuelan citizens don't have. For example the Cuban currency is accepted in Venezuela but in Cuba the Venezuelan currency is not accepted by Cuba.
Venezuela even changed it's military structure to mirror cuba. Cuba really took advantage of Chavez and Venezuela. Granted Venezuela got some good things but no where near a fair deal.
Again Maduro was elected because out of chavez's inner circle he was the most loyal to cuba.