@Kitaman , I'm sorry that Blue Shutters didn't work out for you. It was such a perfect beach day late in a summer that has been short on them, and it was a Saturday, so I guess it shouldn't be a surprise. I know my wife tries to target getting there before 10:00 on the few occasions when she goes up there on a weekday with our daughters, so Saturdays must require going a bit earlier to be safe.
For future reference, if carrying a bike is an option for you, a very nice and well-kept secret is Green Hill Beach in South Kingstown, just on the other side of Charlestown from Blue Shutters. There are only about 8-10 public parking spaces there and they are usually filled very early (especially when it's a good surfing day), but less than a mile straight up Green Hill Beach Road there is Green Hill Park, a public town park that has a parking lot that no one uses. You can drop off Mrs. Kita and all your beach stuff right at the entrance to Green Hill Beach and then go park at Green Hill Park and roll on your bike back down to the beach. When it's time to go, you just ride back to the car and return with it to pick up Mrs. Kita and your stuff.
It's a great little low-key beach in a great little low-key beach neighborhood where we've rented a house for a week at least every other summer for the past ten years or so. The lack of public parking keeps the crowds down, and it only gets crazy crowded for around three hours on peak Saturday afternoons, so unless you're arriving then space on the beach should not be an issue. And you are rewarded by relative solitude once 4:00 rolls around, so if you want to stay through sunset you'll have it mostly to yourselves, except maybe some surfers if the surf is up.