Vegas to Grand Canyon! I have done that in July before.
There is a lot in Vegas that isn't gambling, and its all air conditioned. The Formula 1 pit lane has an attraction and you can race go karts through the pit buildings and start / finish straight. The sphere is great, the amazing shows in many theatres, the bodyworks exhibition, plus the out there architecture of the casinos and internal shopping malls. I think the NBA summer league will be just before the Olympics. You pay about $70 and get to watch multiple games from 3:30 to 9:30. Random shout out for the Atomic Museum, especially if you watched and enjoyed Oppenheimer.
In the summer the Grand Canyon doesn't let people down into the canyon itself to hike because it's hot, dry and little shade. But the south rim is gorgeous, sunrise and sunset are beautiful, and it's higher and not as stifling hot, usually has a breeze too due to the Canyon. They run shuttle buses to various viewpoints.
You can link LA, Vegas and Grand Canyon via some of route 66. Highlights for me are the Oatman highway and Seligman. Then the Wigwam hotel in San Bernadino (LA) or Holbrook (after the Grand Canyon). You'll be in an air-conditioned car so a largely look out the window holiday for a couple of days. But the landscape changes quite a lot.
For LA: I agree with a previous poster that the immediate mile in from the coast is way cooler than even a little more inland.
Whilst everyone goes to Santa Monica, I found the Pier underwhelming and tacky.
I love the Venice Beach vibe though, especially in the early evening (Skateboarding, pickup basketball, muscle beach and the rollerskating crowd). Lots of homeless but they didn't seem threatening to me. I wouldn't hang around after dark though, and there aren't many hotels in that area.
I think you might be best looking around Long Beach for a hotel and driving for the tourist things. The shopping centre at the Chinese Theater is set up well - lots of parking underneath and a clear view of the Hollywood sign (it's quite a way away and smaller than you might think). Access to the theatre and the main bit of the walk of fame.
I've done Universal and loved the actual filming lot (back to the future, Jurassic park, TED, the theme park is fun too, especially the Simpson's land. I've not done the others which are studios only
Hire a car for LA - it's such a car city.
Santa Monica / Venice beaches are big and flat, great for a beach cruiser cycle ride! But I'd be tempted to try some more interesting beaches to the south (that I've not been to) like Crystal Cove, Laguna. Santa Barbara is lovely, clean very middle class and walkable with a pedestrianised high street. Personally I'd go to South LA beaches for a change because I've been to Santa Barbara!