MIT Mathematics Majors have a number of math-centric summer activities available. One option is the MIT Mathematics Department Summer Program on Undergraduate Research, SPUR.
There is a wide range of other "Research Experience for Undergraduates Summer Research Programs," many supported by the NSF, and of summer internships with mathematical content. See the American Mathematical Society site for a listing.
Other summer activities include working as a counselor for a high school mathematics program such as PROMYS at BU.
Summer is also a good time to think about doing a UROP.