OK. This isn't supposed to be a rival for Enty's biking and climbing paradise, nor is it supposed to claim that this is the best biking and climbing area in the North America......
BUT....IF you have a young family (6-12 yr old kids) then you can't beat the Black Hills of South Dakota.
Apart from Rushmore and the Crazy Horse memorial (which is awesome)there are cave and mine visits, horse riding, Deadwood re-enactments, zip line rides great views and some really great bike rides and granite climbs.
The biking can be a little challenging due to very narrow roads (the Needles highway is worth the risk) but the climbing can be very challenging or very easy and I have just taken my kids to an area called Sylvan Lake which has some excellent intro routes. There is a mix of trad and bolted on hard granite.
I realise this won't be for everyone but if anyone wants more info then give me a shout.