There are many, many places to get work done one campus. If you are looking for a quiet place you can always go to Mugar library, which is in central campus. If you are looking for a more social place to do work you can hang out at the George Sherman Union, GSU, which you can do work, talk to friends, and grab something to eat. The GSU is also located in central campus. If you are looking to do some work in between classes you can in various places. There are usually some version of a study lounge in each building on campus so you will always find a place to get work done.
I think one of the best places to get work done is at the George Sherman Union. It houses a food court, so you can grab lunch and then sit down at one of the many tables to do your work. It's also a really central point on campus so a lot of students tend to meet here for group projects and such. It's also right next door to our largest library on campus, so that's really convenient!
The library is huge and has lots of quiet places to get work done. Each dorm also has quiet areas or study rooms. If noise is not an issue then the Student Union, cafeterias, and other locations are good to do work in. If it's just reading then I would offer the gym and get some exercise while getting work done.
Obviously a library. Mugar is the most popular. During the warm months, you could lay down on COM lawn to get in touch with your "earthy" nature-loving side. There are also study lounges in dorms.
My favorite spots are the 3rd floor of Mugar library, the 9th floor of Shelton Hall (gorgeous panoramic view of the Boston skyline!), BU Central, and if you're an engineering student, Ingalls.
BU has great places where you can get your work done. Personally, I always tried not to do too much work in my dorm room (I read some study somewhere that said doing work in your room can lead to insomnia because you associate your room with stress? No idea if it's true, but it was interesting. If anything, I get too distracted in my room and will end up procrastinating). Soo - the GSU (George Sherman Union) has comfy chairs to hang out. The library on campus -Mugar - is probably even better though. There are plenty of places to sit down for long study sessions, and it's open late. However, my FAVORITE place to study is the top of the Student Village dorms for upperclassmen. They over look the beautiful Charles River, and are a fantastic to study in some quiet with a gorgeous view of a sunset over the river.