you can fly to havana via jamaica,grand cayman,bahamas etc.it is not illegal for us citizens to visit cuba but is illegal to spend us dollars there,the new cuban currency is the cuc which is currently around equal to the euro if you change dollars there they will charge you 10% for doing so,this is ONLY for usd so change your dollars to euros in the states and you will avoid both of the above.
Going independently is the best way a return flight from grand cayman is about 200 usd,a tourist visa is about 30.
to stay in the melia cohiba hotel,nacional or parque central(this one is just around the corner from the partagas factory)for a double room is around 140 usd and can all be booked online,alternatively you can stay with a cuban family in a casa particular for around 30 usd per night this can be a lot of fun and a good insight to cuban life
food is generally inexpensive but dont expect too much
the cubans say that the three biggest failures of th cuban revolution are breakfast,lunch and dinner!!!
visit to the factory is around 12 cuc and a trip to pinar del rio to visit alejandro robaina and smoke a cigar from the vega with him on his porch(unforgettable)is a must rent a car for around 80 cuc and you can do the trip in a day
Suddenly a BOTL trip to cuba looks very doable and not too expensive