The Henry Cowell Redwoods State Park (parks.ca.gov/?page_id=546) has miles of hiking trails through old-growth redwood groves along the San Lorenzo River and campsites. The 40-acre grove rises high just 6 miles north of Santa Cruz (parking $10) and it's easily reached on the level 0.8-mile Redwood Grove Loop Trail. The park's tallest is the 282ft "Giant;" look up to spot burls, the "beauty spots" of redwoods, and down to see banana slugs.
