What are you looking to do? Visit an island for the day? Go do touristy stuff? Or enjoy a fly-in meal? The islands offer all, but at different islands. Block Island is where I took my wife for our anniverary, touristy, but very nice people. It definitely gets busy there in the summer, so be ready. Also, departing to the west can be tricky with a full load (heads into a hill) so be ready for it.
Nantucket has touristy stuff to do also. I went there last August and didn't have to have a reservation. It definitely gets busy there also. Martha's Vineyard I haven't been exploring on yet, but flown there a few times with students. Nice people working the tower, I've heard not as much stuff to do there.
Newport you could drive to, but overall lots of tourists come here, so people must like it here. The airport can get busy, definitely more training flights than the other islands.
If you're looking for a meal, find a good $100 hamburger spot and enjoy the day. There are many of these places around here, just ask around.
Overall, all these places are within reach in a single-engine airplane. Keep your altitude up so you can glide to land and you'll be fine. Get flight following, if able, and enjoy the ride. As always, get all the information (noise abatement procedures, etc.) possible before flying out.
For an even better trip, why not visit Long Island? There's an outing that will add a couple hours to your log book and be enjoyable by any taste.
Safe flying.