Don't know if your route North from Grand Canyon will take you through Nevada, but if so I would recommend a stop for hiking at Red Rocks, near Las Vegas. We really enjoyed a trip there a couple of years ago. We aren't casino people so we avoided the Strip like the plague, but there is some nice hiking at Red Rocks. From there you could easily head East past Zion, where there are more awesome hikes to be done. Both areas will be hot when you are there, however, so you will want to plan your hikes for early morning. Also beware of slot canyons when there are thunderstorms about.

I would follow hikermor's advice, he knows a lot about the desert country. One thing I would add is that in my few trips to that part of the world I've found that a fanny pack with suspenders was a good set up. I used one of the Mountainsmith Lumbar models. I put a water bottle on each side and a collapsable water bottle inside. Still room inside it for a lightweight rain jacket, some snacks, a small FAK, and odds and ends. Not having a pack on the back was a much cooler way to hike.