We camped last summer around 4th of July. Weather was perfect - warm during the day (shorts and t shirts) and cool at night (light sweatshirt, pants -- not freezing). But there are A TON of places on the island to stay. Bed and breakfasts, small hotels, or even house rentals.
It was great for kids - every major attraction has a bathroom. Lol. That makes it convenient. But seriously - sand beach, thunder hole, jordan pond, ice cream in town, walking all around the tide pools at low tide - amazing stuff.
We can't wait to go back.