Exit Grand Canyon via Hwy 64 east to Hwy 89 north. The road damage is just beyond the intersection of 89A and 89 toward Page. So you'll need to take 89A west toward Jacob Lake (good practice for you for Hwy 12 :) )and then pick up AZ Hwy 389 west at Fredonia, AZ. Take 389 into Utah and it becomes UT 59. It will take you into Hurricane and on to Virgin. It's a very nice drive with one short uphill getting toward Jacob Lake.
Exiting to get to Bryce which I think is your next stop, you can either take Hwy 9 east out of Zion and go through the tunnels and continue north on Hwy 89 or take Hwy 9 west to I-15 north and pick up Hwy 20 which will take you to Hwy 89. Head a little south on 89 through Panguitch and pick up Hwy 12 to Bryce.
Have fun!