In reply to GJohn:
Windgather is by far the best crag in the Peak for little kids because the style of weathering means that there are many breaks and reach is therefore less of an issue. The grades start from Mod and the great majority of routes are VS and below (though there are a couple of E1s). Routes are only 8-10 m and many are slabby. The crag is only 2 mins form the car and the ground beneath the crag is good for picnics. The only downsides are that it can be exposed to westerlies and it gets very busy at times (including with group use). There is also a small quarry to the right of the crag that offers easy bouldering and short routes (very easy) to get going on.
Other good spots in the Peak...
Stanage around Awl, Been Dun, Bee, Four
Stanage around Deligthtful (left of Twin Towers)
Stanage to left and right of Hampers Hang area
Burbage North
Burbage South (boulders)
Cratcliffe (boulders, but watch the drop off the back of the tor)
Baslow (Small Slab area)
Harborough Rocks
Birchen is OK but many easier routes have undercut starts that are difficult for the very small.