Hey dude, (we've eaten dinner twice but right now I can't remember your name!

)
You're on the right track with this post. This area is really best seen on foot. Every time I get off the bike and go for a hike I am rewarded.
I've hiked in Bryce. It was awesome. I forget the name of the trail, but it was at the end of the road, down past Ruby's. Spent an hour or two tramping amongst the hoodoos. Really great. Lots of other tourists, but that was OK. Only the adventurous ones bother getting out of the car.
I've hiked in Arches. Again, at the parking lot at the end of the road, there's a trail marked "primitive." You follow the little stacks of rocks. Really, really nice. Not a lot of people. There are other great hikes in Arches. I've not hiked out to Delicate Arch (the license plate one) but I bet that's fun too. Might be crowded.
I've heard that Zion has some great hiking areas, and you need to take a shuttle bus to get to them. No personal experience.
Highway 12 seems to have some good trails, but I'm too busy enjoying the road to ever stop. Please if you find good hiking there, let me know. Some day I'll slow down.
I think you can only get to Rainbow Bridge on foot or boat. Dont' know the details, google does. Probably be a nice place to visit if you like natural bridges.
Have a great time, take lots of pix.
Jerry