I don’t know why some of these answers seem too complicated to me. Rather than fly into LaGuardia or Newark (why bother starting even further south?) or New Haven, it’s easier, and may be cheaper, to fly to Boston. As Hanna said, easy public transpo from Logan to Cambridge. Uber or T in Boston. Train to Prov, probably $5 to taxi up to Brown (or walk.) Train to New Haven.
Check flight costs to Boston vs Providence. You could start in Prov, take a commuter up to Boston (or bus) one day. Come back and next day head for New Haven, another commuter (or rent a car, if you’re the required age. It’s much easier to drive south out of Prov than into Boston.) Back to Prov to fly home. But you need to check $ and hotel possibilities.