We are Mancunians exiled in Staffordshire and if you can bear a short trip down the M^ then I'd recommend Trentham Gardens (Jn 15, take A34 towards Stone and Stafford).
Just past the main entrance (keep going south) is Trentham Monkey Forest which is fantastic: monkey colony to walk round, watch them feed, get really interesting behaviour information from the staff. Great little cafe and playground. Then you can go to Trentham Gardens proper for a full on consumer experience, but it is worth then paying to go into the Italian Gardens since they have a fantastic play area there with massive sandpits, drive on tractors (JCB is a local company!), a toddler level 'assault course' and great cafe next to the play area.
Fabulous gardens to run round also
If you don't fancy paying for the Italian gardens, the free bit of the garden (head to the loos in the chalet shops bit and the entrance is there) is also great - walk or take your trike around the lake, go on a boat trip, little train trip etc... Then finish off with a trip to Cadwalladers for an enormous ice cream sundae!
You can spend a whole day (and a whole lot of money!) here and no I don't work for them!
Tatton Park is also great - good playground; Stockley Working Farm - both south of Manchester near A556