The vast majority of no-compete agreements are non-enforceable. Google your local state law to find out more. Practically every large company in my industry has non-competes, and they were never enforced except in egregious cases in which a high level employee left and tried to take a number of employees with him. Even then, the non-compete was tossed by the court and all of the employees were free to leave with no penalty.
If it is a good internship, sign the agreement and forget about it.