jam's right, the Phoenix area in May could be well into the triple digits and there is some serious elevation gain between Phx and the Canyon. Even starting in Vegas and doing your planned tour in reverse would save you some climbing. I grew up in Phoenix and saw a lot of the state and the Southwest. It is beautiful country, but in May you might want to stay farther north than Phx. Northern AZ/Southern UT is at a much higher elevation and stays much cooler.
There's a lot to see in that region too. All of jam's recommendations are excellent. The AZ/UT border is some of the most impressive landscape you'll ever see; red rock, natural arches, and canyons galore. The North Rim is much less developed, has a fraction of the tourists, and offers the same impressive view (it's actually higher than the South Rim, so you get to look down even deeper. If you didn't go as far south as Phx you could certainly find the time for Meteor Crater, spend more time around Flagstaff, Sedona, and the likes, or even head east to the Petrified Forest and Painted Desert (petrified wood is AZ's state rock).
Southern AZ is pretty impressive as well. I love the Sonoran Desert. It's home to plants and animals you won't see anywhere else, but May might not be the time to see it. Growing up, May always marked the start night and sunrise rides.
Where does your Phx to Canyon route take you? Is early fall too late to use your flyer miles, say early-mid October? Phx can still see triple digit temps into October, but generally speaking it's cooler in the south and not quite cold in the north.