@Aimless is relocating? Or just migrating for the season?
I grew up hunting on family land, so I am a bit biased in that private land is the only way to fly when hunting.
Unfortunately I lost access to that due to folks passing on and shady business regarding wills.
Anyway, I am now a public lands heathen. I can't comment too much on anything other than general rifle seasons as that's generally my season and weapon of choice.
You'll have the best luck on public lands if you get off the roads and into the back country a bit. Lots of road hunters here and folks who will hike a couple hundred yards off the roads and think they're practically Bear Grylls.
ETA:
I generally hunt the central part of the state (Price/Fairview/Fishlake, etc.), good hunting all around IMO, just don't expect much Elk on the outskirts of Moab.
Several good units towards the southern end such as the Pasagaunt and surrounding areas. Lots of limited entry stuff there too though.