Second Kilve for a days picnicking, fossil hunt and rock pooling.
Forecast looks ok. There's still walks on the quantocks, make it into a nature walk and spot for deer, birds bugs,fungus, build dams, shelters, hide and seek, etc….
Just beware of the ticks…
Perhaps even pick some worts.
Taunton has little to offer, perhaps a boat ride, play in vivary park, crazy golf there too..
Look up Tropiquaria, could be an experience for them.
But for free, you can't beat the outdoors where you can interact with the kids and get to play a little yourselves..rather than throw money at something and expect that to provide the fun…Which you can do at the http://www.thefunfarm.org/