Two weeks in Utah in April sounds great. I've spent a couple trips to Utah in April and liked the weather a lot. I don't remember it being cold, but it depends on your altitude. We did some great dayhiking in Bryce and Capitol Reef. I barely visited Canyonlands. I didn't honestly care for Arches and Moab that much, it was really hot and super busy, but it's ok. I stayed in a campground in Capitol Reef called Cedar Mesa that I liked a lot: just 5 or so sites, I think, very remote, very quiet, nice hiking. You have to drive down a dirt road for 35 miles to get there, and we barely made it there in our Subaru after a good rain, so 4 wheel drive seems a good idea.
The only backpack I did in Utah was Grand Gulch, so that's the only one I can vouch for. I think it's still protected by what's left of Bears Ears Nat'l Monument, despite Zinke/Trump's butcher job. It was pretty remote and little-traveled, not too hard of a route, LOTS of old native american ruins and pictographs. It's been a dozen or so years since I was there so maybe it's more popular now.
Have fun!