Marbury park (closer to Northwich) is very good, nice walks, lake with friendly ducks, play area and an outdoor swimming pool with kids area. Just up the road from there is Great Budworth ice cream farm, lovely ice cream and low key toys/lego on the lawn for the tots to play with.
At Sandiway there is a mini railway, www.mcmse.co.uk with lovely walks in the woodland. Sandiway also has a very good, free council owned play park.
Delamere has it's own little station so you can catch a train to/from Chester there. There are lots of informal den building areas in the forest now, Go Ape, Segway and bike hire etc. Can be as expensive or as cheap as you like!
There is a lovely outdoor water play park in Chester for the 5 yr old at least.
Cheshire Oaks retail outlet has covered free play areas if it rains.
Walton Gardens is closer to Warrington (but good motorway access) it has a small zoo, play areas, mini golf, ponds, rose gardens and a café. You just pay for parking. There are often inflatables for a small cost.