A lot depends on what kind of time you have. We based in Las Vegas and only spent a day. It’s about a 2 1/2 hour drive. The drive goes through the Majave Desert and the changing landscape makes for a scenic trip, especially when it becomes more mountainous. The first thing we did was take the Zion-Mt. Carmel Highway through the park. For most of the year that’s the only road you are allowed to drive. The drive itself is an experience with many pull offs with observation points...some close to road others you have to hike.
Just east of the tunnel on the road is Canyon Overlook Trail . It’s an easy to moderate trail that’s a half mile out to the overlook. It isn’t that challenging but there are several unprotected ledges that would result in 1000 foot drops. Look at these pictures...
https://www.citrusmilo.com/zionguide/canyonoverlookpix.cfm
The drive was around 15 miles entering on the west side (the side you hit from Vegas) and exits out of the park on the east side. At this point you are around 90 miles from Bryce Canyon. We turned around and retraced the highway back to Springdale. The canyon part of Zion you can’t drive most of the year. There is a shuttle that you take at the parks entrance. The shuttles run every four or five minutes. The main parking fills up in a hurry so the best bet is to park in Springdale. There is a free shuttle service that will take you to the park entrance where you can take the park shuttle.
There are nine stops on the shuttle run through the canyon. Each stop offers a different set of trails. There are some very challenging trails and you’d need to spend several days to get all of them in. There’s lodging in Springdale and the park has a lodge as well.
The two must do trails if you are looking for a challenge is Angels Landing and Zion Narrows.
Here’s Angels Landing info...
https://www.citrusmilo.com/zionguide/angelslanding.cfm
Here is Zion Narrows...
https://www.citrusmilo.com/zionguide/zionnarrows.cfm
I hiked the easier Riverwalk which takes you to the foot of Zion Narrows. If I had more time and wasn’t with my wife I’d have tackled Zion Narrows.
Here is the park guide to help you with your own planning...
https://www.nps.gov/zion/planyourvisit/upload/Zion-Summer-Map-and-Guide-2018-WEB.pdf