Travel to Middletown from either Hartford/Bradley airport (the closest) or the New York airports (at least a 2-hour drive) is not very convenient using any kind of public transportation.
People arriving in NY airports could use the SEM website ride share finder to connect with others to share a rental car. If a car from NY is not possible, one option is getting to New Haven by train (Metro North from Grand Central Station or Amtrak from Penn Station) or limo (Go Airport Shuttle or Connecticut Limo are convenient) and then taking a taxi to Middletown. A New Haven-Middletown taxi will be expensive and you should call ahead to reserve one. Here are the various phone numbers from the Wesleyan University site. Amtrak has a route to Meriden station, which is much closer than New Haven, but it is not that frequent and you should call a taxi ahead of time to get to Middletown. Go Airport Shuttle to Hamden may be closer than New Haven, but check on taxi availability.
We have recently learned of a local service that offers inexpensive service to and from the New York airports: $65.95 for JFK and $75.95 for Newark: Wisla Express, 157 Broad St., New Britain, CT, 860-229-7796, wislaexpress@yahoo.com