I think even at that age kids vary enormously in their tastes, but I can tell you what mine like doing!
In the Warwick area, Hatton Country World is a very good - if a rather expensive - kids' attraction. Umberslade Farm is a more understated version of the same concept. Both are out of town.
In Stratford, kids like eating at Cafe Pasta (Sheep St) and Carluccio's (Waterside), and the Laughing Buddha (Greenhill St). The Four Alls pub at Welford is also popular - just an ordinary pub that does food, but the great attraction is that it is on the river. Further afield, the Fish at Wixford has a fantastic child-friendly pub garden.
Attraction-wise, renting a motor-boat and visiting the Butterfly Farm rank highly in Stratford. Mary Arden's Farm is also definitely worth a visit.
On April 21st/22nd, we have Shakespeare's Birthday celebrations - processions, performances etc. Not to be missed if you are about.
Edited: 6:27 am, March 20, 2012