Sequoia and Kings Canyon both provide many trails for hiking and backpacking, and some facilities for horseback riding.
Suggested Day Hikes:
Alta Peak
Longer day hike to a rugged peak with excellent views.
Most practical trailhead is Wolverton, just South of Lodgepole.
Tokopah falls
Easier day hike to a large waterfall, near lodgepole.
3.5 miles round-trip.
Lookout peak
Easy day hike from grant grove.
Especially attractive in the winter when the road to Cedar Grove is closed, as it affords a similar view.
Mist Falls Hike
A good day hike when in the canyon.