Look into the Hampton Inn & Suites, Middletown, R.I. It's a chain hotel, but trust me, it's a new place and gets very good reviews. It's also a place to consider with a young one, as they have no problem with making your stay enjoyable. Very easy access to Newport from there. I know of Newport B&B's that accept little ones, but unlikely for a 1 night stay in Oct. Check out the Mill Street Inn in Newport if you want to stay close to the action. Good Luck.

I recently stayed at Vanderbilt Hall and there were children and families there. It's an upscale place making it fun for adults too.