Yes, I agree, summer is the best season here if you want to swim. I can get cold (believe it or not!) in winter and it is very rainy. Too rainy and cold to swim. May through Sept. or even as late as Oct. is best. If you can, try to come when school is still in and you'll have the beaches to yourself. :)
We live on the Big Island and it is so awesome here. I would prefer to vacation on this island, personally. It's much cheaper here and most activities are free if not very inexpensive. Our hotels are cheaper or if you want to rent an entire house, you can. It's just so much more affordable.
We have the zoo which is open every day until 4pm and is always free. (Petting zoo on Saturdays) We have black sand beaches on the East side and white sand beaches on the West side. We have snow on the mountaintops that you can drive to, but mostly in winter, not often in the summer, though we did have a blizzard last June. You can drive right up the mountain for free to see the observatories. My husband and I went up and stayed to watch the sun set. It was SO. AWESOME. (Can't take little kids up the mountain, though. Bummer.)
We have an erupting volcano on this island (it's not at all scary like you see in the movies, trust me) which you can go see for only $10 per vehicle and it's good for a week. Free at night if you want to go see the lava in the caldera glowing. Our island is the only one with a volcano.
It's not very touristy here, so you won't see any crowds and there are hardly any tourist areas except a little bit in Kona. We have tropical botanical gardens, waterfalls and lava-heated hot ponds which are pretty neat and fun to swim in. All free.
There is a suuuuuuper awesome playground in Waimea called Anuenue Playground:
Free, of course.
The best snorkeling on the East side is Kapoho tidepools (you MUST have surf shoes - those water sneakers kids sometimes wear) and there is fantastic snorkeling in Kona, especially at Captain Cook.
The only thing you have to pay money for here for the most part is if you want to do something like paragliding, bus tour or other guided tourist activity.