Mt Tamalpais is a hiking paradise. You can download a map of the mountain's trails and get lots of hiking ideas at OneTam (www.onetam.org), an excellent website combining all of the parts that make up the Mt Tamalpais recreation area into 'One Tam.'
One of the best hikes on the mountain is the Steep Ravine Trail. From Pantoll Station, it follows a wooded creek on to the coast (about 2.1 miles each way). For a longer hike, veer right (northwest) after 1.5 miles onto the Dipsea Trail, which meanders through trees for 1 mile before ending at Stinson Beach. Grab some lunch, then walk north through town and follow signs for the Matt Davis Trail, which leads 2.7 miles back to Pantoll Station, making a good loop.
Cyclists must stay on the fire roads (and off the single-track trails) and keep to speeds under 15mph. Rangers are prickly about these rules and a ticket can result in a steep fine.
The most popular ride is the Old Railroad Grade from Mill Valley to Mt Tam's East Peak. Alternatively, from just west of Pantoll Station, cyclists can take either the Deer Park Fire Road – which runs close to the Dipsea Trail through giant redwoods to the main entrance of Muir Woods – or the aptly named Coast View Trail, which joins Hwy 1 north of Muir Beach Overlook. Both options require a return to Mill Valley via Frank Valley/Muir Woods Rd, which climbs steadily (800ft) to Panoramic Hwy, then becomes Sequoia Valley Rd as it drops toward Mill Valley.
For more information on bicycle routes and rules, contact the Marin County Bicycle Coalition; its Marin Bicycle Map ($10) is the gold standard for local cycling.