Take the cilantro, leave the zamboni

Question for you transit geeks: I want to drive to somewhere on the New Haven Line and park my car, and take the train into the city. I'll do it Friday night and come back Sunday afternoon so the car needs to be left over two nights.

What's the best trade-off of distance from NYC, free parking, ticket price, etc? I don't know the parking situation around a lot of the stations, so I'm not sure what to choose.

PS: If you're wondering what I "usually" do, I usually just throw money at either the New Haven train parking garage or the Stamford one, but I'd kinda rather not keep doing that.