I'm planning the same route in mid-September.
What you can safely and enjoyably do in Death Valley will depend on the time of year and the vehicle you arrive in. Around July you should count on high temperatures around 110. This is not an extreme worst case scenario to scare you away, but more like an average high for that time of year at the lower elevations. Carry several gallons of water at all times and you should probably stick to the pavement due to the increased risks of getting stranded in dangerous heat.
Badwater Basin is a must for any Whitney hiker, just because you will want to be able to say you did the highest and lowest elevations in the contiguous United States. This will be hot so don't expect to hike around much. A couple of scenic drives you can enjoy from the air-conditioned comfort of your car are Artists Drive and Twenty Mule Team Canyon. A stop at the Furnace Creek area offers a visitor center, food, accomodations, and some short hikes if the weather isn't too uncomfortable. Nearby there is a paved access road to Dante's Point. At 5000 feet elevation, this breathtaking view may get you a respite from the mid-day heat down below on the flats. Zabriskie Point is also near Furnace Creek just a short walk up from some paved parking. It is a popular vantage point for viewing sunrises and sunsets. Then, depending on how much time you have and your interest, you could consider a side trip to Scotty's Castle for a tour. This Spanish-style mansion with a colorful history was built as a vacation home in the 1920's. Finally, if you haven't had enough hiking you could take the short walk to Darwin Falls on the west end of the park just before you leave. This lush canyon environment will give you a chance to dip your feet in a place that seems starkly out of place from its surroundings.
These suggestions don't even scratch the surface of what Death Valley has to offer travelers in a Jeep in October. But for July I think it would be a reasonably good appetizer as long as you can stand the heat.
