A bike related activity in the actual parks? As far as I'm aware there really isn't really a replacement for riding...I believe there's a kid's game that involves pedaling or something, if I remember correctly, inside Inoventions in Tomorrow Land, Disneyland. Probably not quite what you're looking for. In California Adventures there's nothing bike related inside...
As for outside the park, have you thought about renting a bike? Head towards the coast and there's a few places to rent with nice areas to go through. Huntington Beach, Newport, Laguna and so on are all really nice along the coast.
Where are you staying? If you're near Disneyland you can rent a bike near your place and then take the Santa Ana River Trail which isn't that far from the park. It will dump you off at the border of Huntington Beach and Newport Beach.
Here's a link:
http://maps.google.com/maps?saddr=di...&z=12&lci=bike
I'm not too familiar with riding near the resort so I don't know if the recommended route by google maps is all that great. Maybe others can chime in on recommendations on the safest route to get to the river trail.