| CGM, if I understand your situation correctly, my d had a similar one last year, also in NYC. She had to get all her stuff out of her dorm for a couple of weeks and then move back in to another on-campus residence for a summer internship (she attends Barnard and her summer internship was a Columbia one). Then move her stuff back out for a couple of weeks before school began in the fall.
College Boxes was not an option because they pick the stuff up at the end of the spring semester and store it for the entire summer (or ship home). You cannot get to your stuff during the summer.
Our solution, and it worked well, was to rent a storage unit near her campus for the entire summer. We stored stuff she would not need in the back of the unit (winter clothing, some of her suitemates' stuff, some kitchen stuff, etc), and stuff she needed for summer in the front and therefore more accessible.
We would have used taxis if necessary to move the stuff in, but fortunately a friend has a car in the city and came and helped her move. It took three trips, I believe.
Good luck with this! | 
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