On a nice day, there are several "jumpers" that jump off the bridge, so take your camera to catch the action. The view from the bridge is awesome, and it's fun to walk the length of the bridge (a little scary for people afraid of heights). The visitor information center is nice.
There is a walking trail to the west (and also east, but it doesn't go as far) of the bridge that winds its way past the Canyon Crest and other restaurants/properties on the Canyon Rim. Dogs are allowed on a leash. The trail is paved, good for strollers and roller blades. Take sunscreen and water on a hot day!