You need to make sure you get the latest info about Zion direct from the source. I follow their social media accounts, and this winter has hit them really hard. I think one of the roads into the park (the one that is direct from Zion to Bryce) is closed for repairs for a while. Landslide, or washout, I don't remember. Also, there was a huge rock fall yesterday I think that closed access to a bunch of popular trails. This may cause a crazy crowded par to be a complete cluster, and you may not get to see some of the things you want to see. That said, that canyon may as well be the garden of eden, and is one of my favorite places on the planet, so even a fucked up experience, should be great. Hike Angels Landing if you get a chance. Wake your ass up and do it first thing, before it gets crowded. You need to be on the first bus.
@Anton Chigurh is the resident Utah expert. His rec's were golden on my last trip to that area.
We only spent one day in Bryce, it was cool, but it paled in comparison to Zion for me. Still have not done the GC except for a drive by, so can't help there, but if you get a chance to to horseshoe bend up near page, we really enjoyed it at sunset. Find a slot canyon like Antelope canyon too.