In reply to Danm79:
Cheddar Gorge itself is not the most kid friendly climbing venue.
However, nearby
Ubley Warren Rocks (mentioned in one of the threads linked above) is a good choice with kids - it is shady though, so best on a warm day. There are now more than the 5 lines with bolts at the top mentioned in the UKC crag notes (at least 10 now in the Trench and Pit sections), bolts easily soloed up to or can be reached from over the top in most places to set top ropes, short routes mostly 5 - 6m, the bolted lines probably vary between Mod and HS in standard. I took my 3 year old there this summer and he managed a couple of the easiest routes OK.
It gets occasional use by outdoor groups (hence the bolted Lower Offs) but usually you'll find it deserted, very pretty area close to Cheddar Gorge, outside the limestone trench are good picnic spots and room to run about for kids.
Would also second the "Easy Way Down" at
Wintour's Leap for a larger scale adventure (best done up rather than down, having some previous familiarity with the Crag helps with locating the start), a good stepping stone to bigger adventures in North Wales or the Lakes.