Goblin Valley is great - there will probably be a lot of people there in June and it'll be hot. Be sure you have lots of water with you wherever you go. And sunscreen. And big floppy hats. Little Wild Horse canyon is a great hike. That's all up by San Rafael Swell. The drive on 12 & 24 is great! Capitol Reef is also extremely nice.
I'm going to the big island - really looking forward to it.
