If you are not doing any of the bigger hikes you can do Zion in a day, Bryce in a day and I am guessing the Grand Canyon in a day, did not even think about the Grand Canyon. I have not made it to the Grand Canyon yet so I am not sure how long it takes but I would guess if you are not hiking into the canyon you would be at the overlook(s) for a few hours max? Unless you wanted sunrise/sunset. So, drive to Zion and check it out. Sleep in Springdale (or if you finished Zion early drive to Bryce and stay at a hotel there). Then spend the next day in Bryce (might only be 1/2 a day) so after Bryce start heading towards the Grand Canyon. Not sure where the best place would be to stay for a GC visit.
Use google maps or mapquest to get drive times. I will try and break up a 3 day trip for you but I am in San Jose California heading for Santa Cruz and my ride should be arriving soon.

Enjoy