Unless you have an absolute physical need (such as handicap or health problem), or are staying at a hotel far from campus, don't rent a car! The airport shuttle will drop you off near where the dorm is located, and pick you up there also. There are lots of restaurants less than ten minutes from the dorms. The downtown area is a similar short walk away. You can also take very inexpensive trolleys to most places you might care about.
In addition, parking can be a nightmare around here, in a way people not used to New England may not realize. Many stores do not have parking lots. There is limited on-street parking, and most of it has time limits. It's especially hard to find parking in the restaurant areas; given that there are easier ways of getting there, you'll find that you may not use your car at all. Also, since Providence is pretty small (another surprise if you're not used to the scale of New England), taking a cab to many places is very affordable.
If you do want a car for a vacation, you may be better off renting it just when you need it. There are a few car rental agencies (Enterprise, Avis, possibly others) easily accessible downtown; all major ones are located at the airport. That way, you can use the workshop to find other teachers with whom to make plans, and with whom you can also share the cost of the rental.
If you're staying in the dorms, they will give you parking information. (They have access to a lot.) If you're commuting, please see the computer science department's parking information.