I agree living in Manhattan for sure is ideal for doing shows in Manhattan. But I think it is definitely possible to do internships or shows while living 2 hours away. Inconvenient but possible and doable. I live outside Philly, and I know many people who commute to NYC for their regular jobs from down here, by bus or train. For years. You get used to it. Yes, rush hour lengthens the time, but auditions are generally not during rush hour, and internships also. Also, taking the train helps alleviate rush hour worries.
As far as acting, people definitely go up to NYC to audition, and people who are based in NYC come down to audition for shows here in Philly, and will do shows if something pans out. It’s true if you do a show, it’s a pain to commute up or down, but people do just that if they have to.
Of course if you really want to be based in NYC, you would live in NYC. But if you are talking about which school to go to, I wouldn’t worry about it overmuch. I think it’s wise to widen your choices, and a two hour distance is reasonable. Although as I said, for schools based in Philly, you might want to consider taking advantage of the Philly theatre community (on top of NYC).