San Diego is beautiful and fun to just walk around. The beaches just north of there can be really nice too, but the water is not warm, even in the summer. In San Diego itself, an RV would be a bit much, you might do better to just skip a vehicle in San Diego and then rent an RV when you plan to leave the city.
The drive to Vegas will take most of a day from there, and although part of it is likely to have heavy traffic, once you get past the LA metro area it's not bad. I'd avoid doing it on a Friday afternoon though. Past Vegas is Bryce, Zion and some other national parks that are amazing desert scenery.
Alternatively, you can make a nice loop. From San Diego to the south rim of the Grand Canyon (the part most people think of) which is mostly desert. Then head east around it, see Lake Powell which is a huge man made lake in the desert and worth a day or two, and then head to the North Rim of the Grand Canyon which is a deciduous forest and totally different than the South Rim. Consider renting a boat or jet skis for a day on Lake Powell. From the North Rim, head up to Zion national park and spend some time there too. From Zion, it's a short drive to Vegas. Alternatively, from the North Rim you could heat to Canyonlands National Park, then down to Bryce, then Zion and back to Vegas. It all depends on how much time you want to spend in each place.
July in Utah and Arizona can be HOT, as in 100-110 and very dry so you need to drink a lot of water. Hiking during the mid day can be very strenuous because of the heat. San Diego won't be too bad and the North Rim of Grand Canyon won't be either since it's at a high elevation.
I've spent a lot of time in that area, mostly in an RV. An RV allows you to stay in the parks, and I think you see more of the scenery, but they can use a lot of gas and the mileage charges can add up quickly. I'd suggest mapping out the driving. A rental car and hotels can be less expensive, but hotels near the parks fill up in the summer, so you need to book soon. You also pay for location, so the prices may seem high for what you get. Another plus with an RV is that you can save on meals if you cook yourself.
Once you leave Southern California, there is a huge amount of open space, so driving shouldn't be bad. Just remember, if the driver is on the curb side of the vehicle, you're on the wrong side of the road.
One final thing, July 4th is a big deal. It's fun to be around the celebrations and fireworks, but you need to book early since many people take that week or part of it off and see the parks.