Yes, I would absolutely suggest Newport over Providence if you're stopping in our tiny state. Even Bristol, RI is pretty if you're coming in the Spring/Summer. Visit Colt State Park and Lincoln Place. Narragansett is beautiful, has that classic New England small town feel, and has great beaches, too. And it's tough to beat our seafood (I feel like I have to say this as a Rhode Islander. I actually don't eat seafood.)
This is random, but there's a drive in movie theater here, too. It's kind of in an out-of-the-way area, but it's always fun to see a double feature on a summer night.
https://www.facebook.com/RusticDriveIn
I went to Waterfire one year as well and it was alright. The year I went, Trinity Rep had groups doing random scenes from Shakespeare plays. That was the best part for me, but I don't know if they do it all the time. Now that I think about it, that was like 15 years ago. Sooo... they probably don't do that anymore.
My SIL lives in North Conway, NH (down the road from Kancamagus) and we always have fun up there. Her ex worked here when they first moved up there:
http://www.adventuresuites.com/ Hilarious, but not exactly "New Englandy".
And I LOVE Salem, MA, but I refuse to go in the fall because it gets so ^(&*%#$^ busy. But the museums there are a lot of fun, and educational.