It would be easy to spend a week or more in Zion.... its probably better if you reevaluate your schedule and tell us how much time you want to allocate to each park and then we can help you plan activities for each park.
The through hike of the
Zion Narrows (top to bottom) was recently rated one of the top 10 hikes in the United States by National Geographic, and I'd have to agree, its awesome. I've done it both as a leasurily to day backpack or as a long single day.
Orderville Gulch would also be high on my personal to-do list.
I love doing
Kanarra Creek, which works nicely into your drive down to the park.
Bryce Canyon is much easier. I'd spend two days and do
Fairyland Canyon one day and the
Peek-A-Boo & Queens Garden Trail on the second day. That should also give you plenty of time to visit the popular viewpoints with all the other tourists.