No but I've been there as we hosted a Club 420 North Americans there. But keep in mind the toll to go over the Newport Bridge each way is a few bucks.

On Aquidneck Island (Island newport is on), you may want to check out the following. But I really know nothing about them other than they are there.
Both are probably 10-15 minutes from Sail Newport and an easier drive than dirving from Jameston.

Melville Ponds Campground
401-682-2424
Off Rt. 114 in Portsmouth.
133 sites, fishing, playground, safari field, beach access.

Middletown Campground
401-846-6273
Second Beach, Middletown.
44 trailer sites, immediate access to Second Beach.