Yeah.. the Hanover stop is on campus in front of the Hanover Inn, and 10-minute straightforward walk to the admissions office, but many students live in Lebanon and therefore near the Lebanon stop. They can easily pick you up from the Hanover Inn though. There are also many good restaurants, e.g. Molly's, near the Hanover Inn. And yes, there is a dedicated stop in the South Station. Note though that there is no ticket office in Boston so you shall order online and print out the ticket.
The hospital where you'll spend most of the 3rd and 4th yr is actually at an isolated location, and you need to take a shuttle (Blue line) from the main campus to reach there. I felt that the student tour of hospital is too brief, and I spent only 1.5 hours including lunch there because I have an early interview back at the main campus. So my recommendation is that if you arrive the day before, try take the shuttle to the hospital and take a self-guided tour of it. The hospital is much newer than the main campus building, and is very beautiful.