On the East Coast, you'll likely pay $140/hr for the C172 if it's of modern vintage. Four passengers and bags in a C172 are going to require some careful fuel planning and early morning only flights, even over El Paso. Reliable fuel stops can be 100 miles apart and the thermals will beat you to death after noon in summer. Better plane for the trip would be a 1980s vintage Piper Archer, about 150-200 lbs extra useful load. Neither plane is suitable for the higher Rocky Mountains in summer. Possible routes would be over ELP, (the lowest, doable at 8500'), or via ABQ and highway I-40. (10,500' would be more comfortable westbound around the Sandias.)
Another possibility is along I-80 through southern Wyoming and Salt Lake City, but that's a lot more high terrain, though probably doable at 10,500 in light winds and good weather.
Forget Colorado, I just returned from there, and was playing golf at over 9500' with much higher terrain all around.
Density Altitude at El Paso in late summer can easily top 7500' on the ground. Late summer can be "monsoon" season in the American SW, with many afternoon thunderstorms. Up and down drafts can be severe in the afternoons. Have made many flights between ELP and ABQ, try to be on the ground and sight-seeing by noon.