Duke is not near the beach, but is about 2 hours from the beach. Easy distance for a day trip, May through October. If you like to be outside, you will definitely appreciate that there are lots of sunny days, and more months with good weather than not.
I'm just a student, but after doing my clerkship and an elective, I was very impressed by their psych program. The faculty members are excellent mentors, the residents are smart and supportive. Great variety of clinical experiences, good patient diversity. Durham is not Boston or New York (as has been stated in these forums over and over), but I imagine it's a much funner place to live than Rochester. there are tons of restaurants, a good music scence, beer fest, Durham Bulls baseball, fun affordable neighborhoods near the hospital. Within Duke, I think the psych department is either 1st or 2nd in terms of funding for research . . . considering it's Duke, that's really saying a lot.
Obviously, I know nothing about Mayo, so I can't compare.