I have been to Cuba (8 days) partly to work no yet and enjoyed the visit greatly. Is really a shame that US citizens have to go through this crap mainly due to the ...-kissing of politicians to the Cuban lobby in South Florida. (there I made a political statement so what ??)
You will go through a bit of a culture shock as Havana looks like a '60s movie.
The cheapest way to go is to fly to the Bahamas and fly Cubana from there or alternately fly to Montego Bay or Kingston Jamaica and go by Air Jamaica.(2 flights per day) If you want to avoid US dollars get Euros as these are accepted now, also a non-US Mastercard.
Enjoy Pollo Baracoa, papaya yogurt, roast pork and the very refreshing water-melon juices.
Mike