I’d have to look up the names, but there are some bike trails, including one that goes pretty far down to southern RI. I’m in MA so I’m only sort of familiar, but you might want to check nbxbikes for rentals, they have a Providence location (I got my CX bike from their Narraganset location).
If you’re pretty comfortable with heading out on the roads or maybe drive out of the city a bit, southern RI (tiverton, Sakonnet) going back into MA has some great riding. My parents live in southern MA, so I’ll head over into Sakonnet and pretty much ride along the southern MA coast.
Hope this helps!