From New Haven New York is about 1.5 hours by train; the trains run very frequently, and a round trip ticket is only $30. How often people go really varies. We really don't have any long-weekends built into the schedule, so it can get difficult to spend a day (or two) in New York then be able to get all your work done for Monday, but people do it. I went 3 times over the semester, and I would have had time to go more had I wanted to. I don't really know anyone who goes on a weekly basis, but if you really wanted to there isn't really anything preventing you.
Boston is closer to 3 hours away, trains run somewhat less frequently, and tickets are about $65. People definitely go there much less frequently, and I don't know anyone who has gone unless they were visiting a boyfriend or something like that. Again, that doesn't mean that you couldn't if you wanted to.
Diamond- My classes this semester ranged from 8 - 40 people this semester. Popular intro classes (chem, psych, cog sci, etc) will be big lectures with anywhere from 100-400 people, but in general I think classes tend to be on the smaller side.