Nathan's activity on Insta(last couple of months) indicated he really lean towards east coast not just the most recent bulldog like.
On campus rink is really convenient, it usually will be closed during hockey off season (for renovation etc. but I think the real reason is actually not many people is going to use it during summer break), but I am sure it could make extra arrangement to cater to Nathan's figure skating training. On campus ice rink can provide lots of spare time. their ice time is actually not packed like commercial ice rinks, this means that Nathan may have a ice rink of his own to practice.
about traveling to other rinks to train,
remember even before 2018 worlds, we have spotted Nathan go to quite a few rinks in CA that is not lakewood to train, one of which requires a hour to drive in crazy LA traffic. And Nathan was spotted training by himself without Raf in the other rinks. Nathan also trained by himself for 2 days during OG (with Team's including Raf permission). Traveling hours on the road for figure skating training is a norm for Nathan and Vincent since childhood. they spent hours and hours (more than 6 hours/day for Vincent). it must be nice to have an on campus rink to train.
Coaching, I am glad that this could be an opportunity for Nathan to have new perspectives in figure skating, people and life. Many new possible arrangements can be made, and Nathan can broaden his horizon in many ways. If Nathan will focus more on GOE, SS, TR, choreo, components that is really a great thing I believe every fans would like to see. Many great people(in figure skating community) are located in east coast (New England) and it is closer to the figure skating clusters of Canada as well.
I would not worry about Nathan if he has to train by himself (but I think he will have someone to monitor him). For example, worry about him over-train himself, he has grown as showed in his growth over OG, I have confidence in him and trust him. Also I think Nathan's current PT trainer can easily relocate to New Haven if needed.
EDIT: choose Yale for undergrad, may due to speciall offer Yale give to Nathan. Nathan can also go for the medical graduate school in Harvard or Stanford or whereever he wants if Harvard prefers to recruit from other undergrads than his own, choose Yale would be a great advantage too.