The Canyon scenic drive is pretty nice.
If you aren't looking to hike much, I'd suggest the Court of the Patriarchs as an easy way to see a gorgeous view.
The very best hike Observation Point Hike #7 the view is amazing. But is is very long, switch back, but very tiring, no bathrooms, it takes about 8 hours to complete. If you don't want a strenuous hike, there is a bus that circles around town by the hotels, I believe it is called Springdale. That bus takes you to the Zion National Park, entrance gate. You walk up to the tram and that gives you a view of the park you cannot drive to, in your car. They give you a map that explains the hikes and level of the hikes. The entrance through the park costs $30, but save the receipt (it works for your entire group and) your car going in to the park where the tram doesn't go. Hike #9 is flat easy and pretty Temple of Zimbawa or something like that. The path of that hike goes along the Virgin River and it really beautiful and short. A must see. Another short hike is The Weeping Rock hike #7. This rock never stops raining and view is amazing!
Angels landing hike.
The main canyon area that the shuttles take you through is the main touristy area and most of those hikes will give you some amazing views of the canyon. If you're looking for mainly just overlooking the canyon, the observation point trail is probably the best or angels landing
The watchmen hike is great and easy.
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