Two trails—West Rim and Wildcat Canyon—begin from Lava Point Trailhead in the remote West Rim area of the park. You can reach the trailhead via the Kolob Terrace Road or by hiking the one-mile Barney's Trail from site 2 in the Lava Point campground.
The West Rim Trail goes southeast to Zion Canyon , 13.3 miles one-way, with an elevation drop of 3,600 feet (3,000 of them in the last six miles). Water can normally be found along the way at Sawmill, Potato Hollow, and Cabin Springs.
The Wildcat Canyon Trail heads southwest five miles to a trailhead on Kolob Terrace Road (16 miles north of Virgin); the elevation drop is 450 feet. This trail lacks a reliable water source. You can continue north and west toward Kolob Arch by taking the four-mile Connector Trail to Hop Valley Trail.
Snow blocks the road to Lava Point  for much of the year; the usual season is May or June to early November. Check road conditions with the Zion Canyon or Kolob Canyon Visitor Center. From the South Entrance Station in Zion Canyon, drive west 15 miles on Highway 9 to Virgin, turn north and go 21 miles on Kolob Terrace Road (signed Kolob Reservoir), then turn right and go 1.8 miles to Lava Point.
A special hike for strong swimmers is the Left Fork of North Creek, a.k.a. "The Subway." This challenging nine-mile day hike involves, at the very least, lots of route-finding and many stream crossings.
Like the Narrows, the Left Fork can be hiked either partway up, then back down (starting and ending at the Left Fork Trailhead) or, with a shuttle, from an upper trailhead at the Wildcat Canyon Trailhead downstream to the Left Fork Trailhead. The "top-to-bottom" route requires rappelling skills and at least 60 feet of climbing rope or webbing. It also involves swimming through several deep sections of very cold water.
Even though it is in a day-use-only zone, the Park Service requires a special permit, which, unlike other Zion backcountry permits, is available ahead of time through a somewhat convoluted lottery process. Prospective hikers should visit the park's website, www.nps.gov/zion , click on the "Backcountry Information" link, then click on "Reservations and Permits," followed by "Subway and Mystery Canyon Reservations." From there you will be introduced to the complicated lottery system of applying for a permit to hike the Subway. Lotteries are run monthly for hiking dates several months in the future. Each lottery entry costs $5, and each individual hiker can apply only once per month.
If you're planning this hike at the last minute, try calling 435/772-0170 or checking www.nps.gov/zion  to see if there are any openings. The Left Fork Trailhead is on Kolob Terrace Road, 8.1 miles north of Virgin.