Bryce is in our top 10 list, Badlands doesn't seem to get a lot of good reviews but we spent a whole week there hiking the trails and visiting nearby attractions. We enjoyed it, but that was the summer of what passes for extreme rainfall for that area, so it was not typically what you'll see.
Be warned that April 2nd is very early to be heading out there, I saw a national snow cover map yesterday and IIRC SD was covered. You can expect snow at any time that early in the high altitude parks (Bryce is up to 8000 ft) and the northern parks. Glen Canyon is mainly a boating park with almost no road access. It is lower altitude so snow may be less likely. I assume you can rent boats unless you are dragging a boat all the way from LA.
