Half of Providence's population is Latin American but most night spots are lounges and hookah bars, where little dancing takes place. The Latin dance clubs are fun and predominantly Dominican, so it's mostly reggaeton, bachata, and merengue playing there. A little salsa, but not much. There are a handful of salsa dance groups that hold events and lessons here. There's also a group called Providence Tango, located in nearby Pawtucket, that holds regular events and lessons. And a place in Somerville, MA (about an hour away) called Boston Tango that is very popular and hosts fun milongas. The Boston metro area is teeming with Brazilians, so you should have no trouble finding great options for that scene.