It's almost 3 hours into Manhattan from here (Ledyard). As an ex-pat Bronx girl, I make the trip a lot. The train isn't any quicker really and costly. So a daily 6 hour round trip, it better be a reeeeally good job.
Commuting between Ledyard and Manhattan is possible but probably not realistic. Taking the train is an option but it is a 2 hour train ride. That being said, there are those that do commute to the city during the week but generally not on a daily basis from Ledyard, CT.
It is 130 miles from Ledyard to Manhattan. The train would be the best bet, but it would require you to switch trains from New Lodnon to New Haven, then New Haven to Manhattan. I have taken the New Haven/Manhattan train, and that alone is 2 hours. It's about 1 hours without traffic driving from Ledyard to New HAven. Then, there's always traffic on I-95, especially during the summer months.
Not completely unrealistic but the job that you're commuting to must be well worth it. Typically, the income earned in NYC is greater than that earned in Southeastern CT thereby making home-ownership in Southeastern CT more affordable with the NY inclome. Commuting specifically from Ledyard may add an unnecessary 15 - 20 minutes to the commute depending on the location in Ledyard. It makes more sense to live closer to I-95: Niantic, East Lyme, New London.