Excuse me if I 'm wrong. Am I getting this straight?
Dad wants to live in a peaceful shoreline setting, you want to work in NYC as a personal trainer. You're planning on moving here in a year or so, but then you eventually want to move out and away from Dad and toward NYC for the arts scene and work.
We can easily keep Dad happy. There are a number of choices where he can find that little shoreline town with a 4 bedroom home on an acre with taxes in the $ 6,000 range.
Your best bet, IMHO, is to move to the shore and look in the New Haven area for a job. As has been pointed out to you, commute to NYC daily is not feasible from the shore east of New Haven. It just takes too long. You also have to realize that commuting costs money. If you're a new trainer starting out, you would most likely likely start out as an employee at a health club or private gym. The salary is not great, but OK for a young person starting out, if you get some benefits, but commuting is going to eat up a huge chunk of it. Better to stay closer to home and sock some cash away. Personal trainers only make money when they built up a personal clientele and can charge by the hour. But that takes years. All those cultural activities you want are not necessarily free to go to. Better to stay close to home and have some salary left over to use on them.
What you have to realize is that CT is not a cultural wasteland. There are galleries and theaters, music etc. all over the place. Hartford has much, the shoreline out through Old Saybrook, Old Lyme to New London has many artistic opportunities
New Haven is in a class by itself. There is so much to do you won't have time for it all.
Consider living and working in the New Haven area for several years. When you get some work experience, then maybe think about moving out on your own and renting a small apartment in Stamford and taking the train to that job you want in NYC. That's the only way that's going to work. You would have to live in an apartment to be anywhere with a decent commute to NYC. Nothing wrong with wanting the NYC live & work experience. However, it is so expensive to do so for a young people just getting started, that very practical considerations have to come first.