You would best to avoid summer if you don’t want to be burnt to a crisp! Spring and autumn are the best times heat-wise, although the occasional snowfall that winter brings makes the red rock even more beautiful (if that’s possible!)
Monument Valley is a Navajo Tribal Park, not a US National Park so make sure you are respectful of the local customs and traditions. Photography is allowed but when taking pictures of Navajo residents, ask permission first as a contribution is expected.
See sunrise through Masa Arch in Canyonlands NP, watch a breath-taking sunset over the Delicate Arch in the Arches National park, hike up Angels Landing in Zion National Park, then to top it all off, take a limo ride down the Vegas strip!