Numerous airlines fly into the Providence, Rhode Island airport (T. F. Green / PVD). PVD is about an hour away from Stonington, and since there is virtually no public transport in Connecticut, you'd probably need to rent a car. The other airport option is the Hartford, Connecticut airport (Bradley / BDL). Bradley is also about an hour away from Stonington, and not as nice an airport to be quite honest. (Stonington is very close to the Rhode Island state line, which is why we always fly in and out of Providence.)

Amtrak runs through Stonington, making a stop in Mystic (MYS). You would need to call a cab to get from there to your hotel, but it's pretty centrally located in Mystic.

From the sunny South:
Take 95 North all the way to Connecticut exit 90. This is the Mystic exit and will deposit you right in downtown Mystic.

From the cold North:
Take 95 South all the way to Connecticut exit 90. This is the Mystic exit and will deposit you right in downtown Mystic.

From East and West:
Who comes from those directions? If so, you're on your own.