I did my undergrad at Yale, so I can comment on (2) for what it is worth.
I think that New Haven would be an absolutely terrific place to go for graduate school. It has easily enough bars and restaurants, between the chapel street area, broadway area, and wooster square. There are many music / art / cultural opportunities, through Yale and through the city. There are a couple of clubs, although that is not the focus of the social scene. It's a small enough city that there are some really pretty, nice neighborhoods (Wooster Square, East Rock). And despite being a city, it's easy to get outside and into nature for hikes and the like. And the price is right; it can be a pretty inexpensive place to live, both in terms of essentials (rent, food) and discresinary (bars, restaurants).
I love the fact that New Haven manages to balance all of these positives, but the flip side of that is that it isn't "the best" in any one thing. It's not even on the same scale as a New York or San Francisco in terms of going out and culture. It's nowhere near Dartmouth in outdoor activities. It probably doesn't compare to Madison WI or Ann Arbor MI if you're looking for a cute neighborhood to raise a family. But I do think it balances these things very nicely.
In terms of transportation, a train ride to NYC is ~$15/1.5Hr, and a shuttle to Bradley Airport is maybe $20/1Hr. There is an airport in New Haven (Tweed) but it's flights out of there are pretty limited. Budget busses to Boston and New York also exist, for $10-20 or so.
There are negatives. There is crime, and while I never felt threatened, muggings happen and there is ocassional violent crime. This never bothered me, but if you get seriously uncomfortable with this, then New Haven might not be a good fit. The medical school is on the western edge of campus, which isn't as nice as the area right around the undergrad campus. If you decide to work in a thesis lab that is on science hill, you might end up needing a 15-20 minute shuttle ride to get there. Not a dealbreaker, and probably not as bad as a place like Harvard, but not as nice as a place like Penn, where everything is right there.
Let me know if you have any specific questions about New Haven. Also, it would be useful to know where else you're considering, if you want to compare and contrast. Hope this helps.
