A lot of different things go into a kid choosing where he wants to play. It isn't just exclusive to New York. I think the main factors are 1) Does he feel comfortable there and 2) Does he like the coach?
Because, you don't want to go somewhere that you don't feel comfortable and don't fit in. When I visited Ithaca, I felt comfortable right away and realized that's where I wanted to go to school. When I visited a certain SUNY campus, which I won't name, I didn't feel comfortable there and felt like everyone thought they were better than me.
And with the coach, you're not going to choose to play for someone you don't like. You're basically paying to play baseball unless you have a financial need-based scholarship. And even then, you're still paying to go to school. If you like the coach, all the better. Say I visit school A, everything seems good there, but I'm not really a fan of the coach for whatever reason. I visit Cortland, meet Joe Brown, like him a lot and like the campus. Chances are, I'm going to consider going to Cortland.
And with the pay to go to school, that impacts your decision too. Some schools are just out of kids price ranges, even with the financial aid packages schools give out these days. A SUNY school may be more financially attractive than a private, especially with the stark difference in tuition costs.
There's also academics and what major people want to explore. Division III's aren't baseball factories so you're actually going to be using your degree after graduation. You hopefully want to go to the best school for your major. If you want to be an engineer, then you might consider RPI. If you want to be a baseball coach, Ithaca, Cortland or Brockport are all good options. And other schools are good for other things.
In the end, you want to pick the best school possible for your development, both as a person and as a baseball player. Sure,playing baseball is great in college, and when you graduate and don't go pro, you've got a solid education to fall back on. And those baseball experiences can always be translated over to life and where can you best prepare for life.
Jeez, I should work as an admissions conselor or something. How'd I end up as a baseball broadcaster LOL