My school is one of many in the Boston area. It is about 10-15 minutes walking to Fenway park and a T ride away from main attractions like the Aquarium or Museum of Science. Simmons students are part of the Fenway College group so we can get into museums like the Museum of Fine Arts and the Isabella Gardner Museum for FREE. If you purchase tickets for other attractions through the student center you can also get some pretty good discounts. The Boston Public Library is also just a few T stops away (very walkable on a nicer day) Surrounding towns are not as far away as I originally thought and there is a winter Farmers Market in Somerville, its fun to walk around Harvard Square (both of those accessible by bus) and if you want some music and arts scene I have found more of that in the Brighton and Allston areas (easy T ride). There are a ton of art/performing arts schools, Emerson College is by Boston Common and has shows going constantly. The symphony can be heard by walking about 20 minutes from campus.
Still finding my own gems of restaurants and bars, but also a wide array of shopping available including some second hand shops. Don't forget the North End in all of it's Italian delights. The two big pastry shops, Mikes and Modern can get a little hectic, but worth the wait either way.
For the sports fans, TD garden hosts the Bruins and Celtics (at the North Station T stop) and Fenway park of course is right down the road from campus. Patriots day, the third monday in April, commemorates the battles of Lexington and Concord while offering the Boston Marathon followed by a Red Sox home game all in one day! Everyone is out to support the runners (professional and fundraisers).
It is a very athletic city in general. People love to be outside playing all varieties of sports. Students make up a large population of the city so you will more likely than not be assumed a student (you will still have to ask for student discounts). The best way to see it is to get out and walk. The city is totally walker friendly and you are more likely to see the hole in the wall burrito place or awesome variety store if youre strolling by.