Is there a room service menu? Are Vinya and Rosmarin the only options for dinner inside the hotel
They do have a restaurant in the hotel, but would recommend walking around. There are at least a dozen different ones of varying cuisines and prices within a few blocks of the hotel. Most are not chain hotels and provide a quaint insight to Providence.
I would walk around. Lots of good options in providence!
They do have room service (or "in room dining" as they call it) and I would imagine that this food would be only from the restaurants in the hotel. As Jan M. points out, there are a plethora of really, really good restaurants in the immediate vicinity.
Get an answer from Hotel Providence staff and past guests.