Zion in early June was hot on the mesas but cool in the canyons. A day trip up the narrows shouldn't require a wetsuit but you will need a stout hiking pole, good shoes with mesh as they will be submerged 85% of the time. Neat trip though. Bryce maybe nice depending on snowpak this year.
The Canyonlands Chesler park area is dry but a parking lot is central to this area, so a trip around it, using your car for emergency water is possible.
Looking like a dry winter for the entire Western USA right now however.
(ed: caps)