That is a hot time of year to travel across the south! If you are into history, you might like taking the Route 66 adventure- it offers some great stop-offs along the way. Then you can break off around Oklahoma City and head to Memphis and on to Atlanta.
For the next leg, you could go either the coast route or inland...coastal roads will be crowded and lodging expensive, but the east coast is way different from the west and you might enjoy stopping in some of the quaint communities like Beaufort, SC and the Outer Banks of Nc as well as Charleston and Savannah.
Interior route could take you up the Skyline Drive and Shenandoah Parkway through VA, probably want a stop in DC for a day or 2, then on to NJ and Philly.
To return, try a northern route.
For some other insights and really sound/specific advice, Trip Advisor has a "road trip" forum where folks discuss this type of trip with regularity and there are a couple posters there who travel the US extensively and can give you specific hotels in specific cities and some of the really unique "roadside attractions" along the way.

Have done RT to/from Bakersfield to Atlanta area twice. First night Flagstaa, side trip to Grand Canyon if you haven't been. Next Albuquere if you want to spend some time in Painted Desert-Petrified Forrest Nat. Park. Or, if you want to push, Amarillo. Personally don't see much to stop for in Oklahoma, but I'm sure others can point you to points of interest. After Amarillo it was Little Rock for us then Memphis where we left I-40 for US 72 into Chattanugga and I-75 to Atlanta.

Thank you so much for this advice. Will be seeing family in Atlanta, New Jersey and outside of Phila. Will take one route then return on another so that we can see a lot of the US.

You have enough time to drive to Yellowstone and Grand Tetons and then over to Mt. Rushmore and the Badlands and head east on I- 90 going one way or go through Vegas and north to Zion, Bryce, Capitol Reef, over to Arches and Canyonlands then I-70 through Colorado with stops along the way, maybe St Louis.

I've done 90 from Minnesota to S. Dakota and 80 from Wyoming to Pennsylvania and found 90 much nicer in terms of traffic fwiw.

I went on my cross country trip going west many years ago. It was also July. We just drove to the next stop some days and spent a night or two in some places. My favorites were Memphis, Grand Canyon and Las Vegas. Of course where you stop may depend on if you've been to any place along the way before.

We were ok with winging it - there is usually a place to stay at a highway hotel. It helps to have the AAA books and maps to consult along the way for this.

L.A. to Atlanta in July? Make sure your car's AC is working!
Then going to Philly, then back home. Hmmmm....
Places along the way that *I* have enjoyed -- your enjoyment may vary.

Las Vegas
Grand Canyon (buy your "America the Beautiful Pass" as you enter)

either this -- shorter and less heat but almost nothing to see
Petrified Forest NP
Then LOTS of driving on I-40
Memphis (music & BBQ)
US Highway 78 to Birmingham, then I-20 to Atlanta

or
Phoenix, Tuscon
White Sands NM
San Antonio, Austin
Houston
New Orleans, then I-20 to Atlanta

After Atlanta
Great Smokey Mountains NP
Shenandoah NP (created for cool vacations in the summer)
Washington DC
Fort McHenry
Philadelphia
West on turnpikes
Rock & Roll Museum, Cleveland
Chicago
West on I-90
Badlands NP
Black Hills (a LOT more than just Mount Rushmore)
Yellowstone & Grand Tetons

At this point you need to ask, "How much more can I take?"
If the answer is, "Just get me home!", then follow I-15 back to L.A., making quick stops at Bryce and Zion. If the answer is, "Bring it on!", then back on I-90 and head for Seattle.
Seattle
Olympic NP, Mount Rainier NP
Portland and Columbia River Gorge
Then follow I-5 back to L.A., stopping at either S.F and/or Yosemite.