We've had some nice replies on Facebook & Twitter.
Soundsteps Music School says "Surrey has some super bluebell walks, kids love that

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Haslemere Museum told us about their lovely gardens for a picnic and grounds for a short walk with tree and garden trails. They also have a brilliant observational beehive where children can lift off the covers and see what's happening inside (bees safely behind glass so you won't get stung!).
For my part, my family really like all the local National Trust properties and RHS Wisley. They all usually have nature trails and activities laid on to help children get back to nature, and their play areas are usually of a more rustic nature inspired by the great outdoors, eg the den building at Wisley's play area and Hatchlands new willow play area. We'll also be rock pooling in Wales for some good old fashioned fun in the summer holidays, not sure how many rock pools there are in Surrey though!