Zion is well known for great hiking, fantastic scenery, and truckloads of people. We'll guide you through the best parts, and maybe some of the less-traveled (but just as fantastic!) paths.
Floor Valley Road
Most of the popular hikes start along the Floor Valley Road (also known as the Zion Canyon Scenic Drive). As of now, passenger vehicles are not allowed on the road, so you will need to either use the Zion shuttles or hike/bike your way in. Getting to the end of the road and the Temple of Sinawava is something like a 6 mile trek, so we recommend either the shuttle or a bike.
If you want to take the shuttle, understand that it's first-come first-served, so you may find yourself waiting in a long line. Going early in the day will improve the situation somewhat, and the queue also drops off starting early afternoon (though by then you won't have much time to hike!).
You'll want to consider Angel's Landing and The Narrows, but these can be grueling. In particular, The Narrows requires wading through somewhat high water levels (depending on the season), and you may want to stop by the local outfitters beforehand for some dry pants and boots. The Emerald Pools offer a more relaxed hike and varied scenery, so they are not a bad choice either.
Points of interest here include:
• Emerald Pools and related trails
Expect to see lots of fellow hikers along all of these trails.
Zion - Mount Carmel Highway
Driving through on the highway is actually not a bad way to see some cool portions of the park. There are numerous pull-outs for short hikes, photo opportunities, or just staring out the window as you drive through. Beware that some of the parking lots fill up quickly, particularly the Canyon Overlook right before sunset.
Zion's Outskirts
You can also explore the outskirts of the park to get away from the masses. Kolob Canyons offers hiking trails for everyone - they range from easy and short to long and hard. It's still a park with paved roads and a visitor center, so expect some crowds, but it won't be as packed as Zion proper. Other, more rugged trails start a bit south of that. These extend into the center portion of the park too, into what's known as the Kolob Terrace Wilderness, and offer great long-distance hiking or backpacking options.
South of that lies The Subway, a permit-based hike that you can attempt if you are a bit more adventurous. You can go top-down or bottom-up. The bottom-up approach only requires some pathfinding, but going top-down requires rappelling gear and likely a wetsuit (you'll be doing some swimming). That said, you won't see all of The Subway if you go bottom-up, so don't put away your ropes just yet.
If you're looking for camping, there are lots of dispersed camping sites along the road leading north of Virgin towards The Subway. Someone at a BLM office can point them out to you as well. These offer a convenient place to stay near the park if you're into boondocking (or you couldn't get a reservation inside the park).
On the eastern side, you'll find more overlooks and good backpacking options with fewer crowds. You'll be a bit higher here than the other options, too, which has its own advantages. Expect to be driving on dirt roads for several miles to get here.
Points of interest around Zion's outskirts include: