Swindon is down the road, and has a couple of really nice parks for kids. Lydiard has a great play area and a Jungle Parc which is basically Go Ape for kids. £12 per kid, my boy loves it there.
Coate Water is Marlborough side of town and has a miniature ride-on steam railway, a splash park and crazy golf.
If the weather is bad and you like trains / industrial history, the Steam museum is worth a visit. It’s right next to the Outlet Centre which could be of interest to family members not wanting to look at steam engines.
If you go to Oxford, check out the Natural History museum, at the back is the Pitts Rivers museum which you have to see, if only for the shrunken heads.
If going to Bristol, Clifton is nice, the zoo is good and the Explore science museum is great for kids (but quite pricey).
Also worth a visit, about an hour’s drive from Marlborough, is the Cotswold Wildlife Park.
The New Forest is a bit of a trek, if heading that way a good family day out is the Moors Valley park, near Ringwood. Fantastic play areas and another steam railway. You can hire bikes there too for the bike trails and there is a Go Ape.