Point Reyes is not an awesome mountain biking destination, rather it is a great vacation place with some mountain biking opportunities. The Sierra Club has pretty effectively limited the areas where mountain bikes can go, however there are a few places to ride that are worthwhile.
I was with my wife so most of the rides were pretty low key. There are a few nice mellow rides to the beach, and one trail with sone pretty wild singletrack.
National Park Services has a nice Point Reyes Web Site
On our first day at point Reyes we started at the visitors center and rode the Bear Valley Trail towards the coast. At the time we weren't really trying to get to the beach, if we had been we would have been disappointed. About .8 miles from the beach is a nice bike rack and 2 trails to the beach. Neither trail allows bikes so bring your lock and plan to walk the last portion of this trail if you want to go to the beach.
Other than the fact that the trail doesn't quite make it to the beach this is a nice trail. There is some fairly tame climbing and it is all fireroad so you might consider bringing your kids here. The trail is very well maintained and follows along a couple of streambeds. There are plenty of places to stop and rest and bathrooms about 1/2 of the way to the beach.
We spent a little time in Point Reyes Station sucking down some lunch and then headed for the lighthouse. Right before we got to the lighthouse Fiona spotted a short mountain bike friendly trail out to Chimney Rock.
The trail to Chimney Rock was very short, probably less than 2 miles round trip but it was a fun little jaunt. The trail is singletrack and has a couple of short steep climbs and a few little rocks but nothing the average 12 year old couldn't handle. When you get to the lookout point you are treated to incredible views of Drakes Bay, the ocean and some really cool rock formations immediately off the coast. This trail was not one you brag about in the pub but we brought the bikes and had decided that anywhere we went it would be on two wheels. Definitely worth the detour.
On the way back to the Hostel for the night I decided to ride a portion of the way back. Fiona dropped me off on the top of Mount Vision and I took the Inverness Ridge Trail from the peak of Mount Vision back to Limatour Road with the mistaken impression that it was a tame fire road descent. Indeed there was a considerable descent the trail drops about 1000' in about 3.8 miles. The trail was mostly tight singletrack with butt on rear-tire steep descents and climbs so steep you have trouble keeping traction on your rear tire. (Photo from Bear Valley Trail)