I don't live in Natick anymore, but there used to be a summer evening concert series on the town green geared toward kids (& free).
The community organic farm in S. Natick is also free-you can visit pretty much anytime, though they do also have camp in the summer and depending on the time you choose to go, it can get crowded.
You can swim at Dug Pond if you purchase resident/guest tags. Farm Pond in Sherborn is nicer and I think they have a limited number of non-resident tags available every year.
"Weezie's Garden", a child's interactive garden/play area at Elm Bank in S. Natick (entrance is technically Wellesley) is also fun and free. There are walking trails through the woods, and one can stroll around the gardens and picnic, etc.. It's leased by the MA Horticultural Society and is open daily. You can bring bikes or ride-on toys too. Except for special programs held there, it's all free.
If your parents are nature lovers, they can take walks through Broadmoor Audubon Sanctuary also in S. Natick.
It's always fun to grab a snack at the coffee shop by the S. Natick Dam, sit and watch the water fall and the canoes on the Charles River and eat your picnic.
There is a small but interesting museum in the basement of the S. Natick library that includes a lot of local history. Check their hours. I think it's under the jurisdiction of the Natick Historical Society. I think they ask for a small donation.
Summer in S. Natick was always my favorite time of the year, because so many residents desert it for the cape and islands!