based on the data on wikipedia (not sure where else to easily find it) and using what you gave for a definition, the providence urban area roughly includes cranston, johnston, smithfield, lincoln, cumberland, pawtucket, central falls, east providence, barrington, warren, tiverton, little compton, warwick, west warwick, coventry, east greenwich, north kingstown, woonsocket, and bristol (in no particular order, obviously). i didn't find the data for the nearby towns in MA. as you can see, that's almost all of RI. it may also include portsmouth, middletown, and newport.
that's only the contiguous area as well, not including narragansett or westerly.