Should be a neat trip. Lots of interesting country ahead of you. You will see temps around 100F in the lower elevations of AZ and New Mexico at that time, and afternoon thunderstorms during that period. I would recommend having some sort of light weight rain gear (upper body only) handy.

I would also recommend a full brim, light weight hat, preferably cotton for routine wear. You will appreciate the costant shade. If it gets really hot, soak the hat for cooling effect. I prefer lightweight, full sleeve shirts for these conditions.

I would carry a minimum of two liters of water on just about any excursion (you can make an exception for the 1/4 mile trail next to the Visitor Center, but that's about it) and pack more for longer trips, especially if there are no known water sources. You will be new to the arid conditions and will need more water until your body adjusts. It is better to be safe than sorry! Be sure and tank up in the evenings - it is easy to become chronically dehydrated and that isn't any fun.

If you are looking for out of the way places, I would recommend the area around Harrison, Nebraska - Fort Robinson, Toadstool Park, and a good gateway to the Black Hills (where I will be in July, digging away - drop by if you like).

I would also recommend Canyon de Chelly in NE Arizona, one of my all time favorite places. Sorry, no info on Dead Horse Point - I am a vast void of ignorance - all I know about DHP is what I have seen in the movies.