We will be in the Jackson area a week before you. Looking forward to it. As far as temps in Utah and NM, that's tricky. Depends on where you'll be going. Here is some known average data.....
New Mexico average temps in June:
75 37 Eagle Nest
83 47 Taos
84 49 Santa Fe
94 64 Carlsbad
88 62 Albuquerque
Utah average temps in June:
75 45 Bryce Canyon Park Headquarters
89 57 Canyonlands Park, The Needles
86 58 Capitol Reef National Park
93 58 Moab
96 62 Zion National Park
Good luck and safe travels!
- Mike