GAJ, I suggest staying in Newport and taking the shuttle over to Jamestown for the day. The Jamestown/Newport ferry runs right out of Newport harbor and brings you right into the "downtown" area of Jamestown. Another suggestion depending on whether you have your own dinghy and what size it is would be to dinghy over to Jamestown. With the right conditions it's an easy ride. I've done it just to go grab ice cream on the other side. I would not suggest this with a small dinghy or motor.
Jamestown is nice but there is not much to do. Also, as Prospective mentioned the marine there is very open to the wind and wakes. you'll be rocking and rolling all night.