Going to Cuba is not all that unusual. You can go with a tour group, for cultural/educational/humanitarian purposes. Or you can fly to a country that has direct flights to Havana (like Canada or Mexico), and buy a ticket to Havana there. But, you can’t spend US dollars there (by US law) and you need to be sure the Cuban immigration guys don’t stamp your entry visa into your US passport. That would be a giveaway when the US immigration folks look at your passport once you return from the in-between country.