It'll be hot in the desert...
Hello ToddB
Just as a note, it'll be warm in the desert in August -- probably around 100F. So be prepared. (*laughing at myself* My usual cautionary note to folks it seems...) Drink lots of water!!
Given a couple of extra days in SoCal, you have some options on where you might go, or what to do.
Given an extra day and a night, you might go up the coast through Santa Barbara to Hearts Castle, near San Luis Obispo. That's a several hour drive from LA, but very doable, and lets you see Santa Barbara Mission, some of the Coast, and Hearst Castle, plus perhaps the Elephant Seal Colony at Pedros Blancos about 10 miles north of Hearst Castle. From the San Simeon area (Hearst Castle area) you can cut east across the state to Las Vegas, with a drive of around 7 hours drive time (plus gas, food, sightseeing, bathroom stop times) -- that's compared to 5 hours drive time from LA to Las Vegas.
Another option given an extra day and a night is to swing up to Sequoia National Park, or even Yosemite, before heading for Vegas.
Or if you want to spend time in the desert, you have the option of swinging through Palm Springs, and thence up along the Colorado River to Vegas, or going through Joshua Tree National Park, or visiting Death Valley, or the Mojave National Preserve. Again, I do want to just point out it will be hot in the desert in August, and that you should be prepared for it. Desert visits and driving, even in the high summer, is very doable -- but you need to be prepared with extra water, a cell phone, and a vehicle in good mechanical shape. To just about everywhere the roads are paved and usually in pretty good shape, and there are lots of services along the main roads. I'd be more careful about going off the paved path just in case in the summer, just in case.
Thanks for the suggestions
Thanks to both for the ideas. No matter how we go I will take plenty of water!