take Hwy128 east to trailhead. Hike up to Morning Glory arch. Corona Arch is a quick hike off of Hwy 279 (it's the place where the rope swing videos are shot).
Fiery Furnace in the park is cool too. You need to reserve times at park entrance though.
Last time out we did Ring Arch and The Tunnel, but they are off the beaten path and you have to do your own route finding. Check our climb-Utah.com for some other ideas that will get you away from the crowds.
Of course, the standard stuff is worth doing in the park for first timers.....Windows, Devils Garden, etc. Delicate Arch is good too.
Hydrate, hydrate, hydrate.