If you just want to fly for pleasure just get a piggyback
http://pilots-paradise.com/guide-to-obtaining-an-faa-ppl/
You can only do it once so if you have an airplane licence and a helicopter if you piggyback the airplane licence you have to do the hour logging and check ride to get an FAA PPL (H).
Best way to organise the piggyback seems to be to arrange to rent from an FBO experienced in these things, they will sort the paperwork - also the essiential flight review (simultaneously with the check for rental).
You do not need an FAA medical - the liscence is valid so long as your EASA liscence is valid (medical and review) AND you are in FAA flight review.
Works with any ICAO licence - several of my friends have piggybacked off Barbados licences to fly N reg between the islands.