hi there,
TF Green Airport (Theodore Francis Green Field), which is located in the city of Providence is your most likely landing airport.
You can only fly to Rhode Island on commercial flights from outside of the state into this one airport. It is a fairly large facility with multiple national franchises for car rentals, and is within just a few minutes drive of many
Providence hotels.
Also, you might consider flying into Logan Airport in
Boston. It is just over an hour's drive from Providence, and it is definitely a viable option.