As someone who has spent time at GC, I'd say go for Zion. You CAN do the tourist thing and peek over the edge at GC but I think you'd get more in depth with dayhikes at the other locations.

If you go to the GC, I'd suggest South Rim. Stay away from the circus around the hotels and Bright Angel Trail. Go to the new Visitor Center and walk to Mather Point because it IS a great view. Then head out the S. Kaibab Trail to Skeleton Point. It's a good half day hike for most people. (Remember time back to the rim is about double time down the trail.)