Tour-of-the-Trikes (TOTS) that happens in June.
RAGBRI in the midwest, riding across the plains and many others.
Check online or contact your local recumbent shop. There are meet up groups and you could always start your own.
RIDE WITH LARRY is a group raising money for Parkinson's research in South Dakota. 300 miles across the state by trike...larry and his friends raised a great deal of awareness as well as money about the opportunities for people to stay mobile, active and have FUN!