In reply to LastBoyScout:
Kids love Brimham Rocks if you don't know it? No need for climbing gear as it's a natural playground. Be prepared for some 'how the hell did they get up there? And how do I get them down?" moments mind you. I can think of a few kid friendly routes but you need to hunt them down.
Brimham's a bit of a drive from Ilkley though. So for climbing climbing, I'd go Rocky Valley. I can think of diffs like Long Chimney I took my kids up, or clambery no start Holly Bush route on the biggest butress, Three Slabs Route, Flake Climb.
A lot less full of people and less of a fish bowl than the quarry. Routes are over a steep slope and feel like climbing. It's a nice walk in from the White Wells car park too or from the Cow and Calf. Main downside is that depending on weather and time of day, these routes can be defended by a fierce army of midges...