Road trip to Los Angeles to Texas to South Dakota and back to Los Angeles what to stop and see?

SD to LA is 23 hours driving if you are driving the speed limit the entire time and not stopping for gas or breaks.

Driving to Amarillo, TX from LA is 16 hours without stops

And Amarillo to SD is 12 hours without stops.

LA to Amarillo is 2 days and 1 night

Amarillo to SD is 1.5 days and1 night

SD to LA is 3 days and 2 nights.

As you can see, at most you have 2 free days, which are likely for the wedding....

What part of Texas are you going to?  Google some towns you might go through and see what is in the town.  I think the Grand Canyon would be worth the time.  After leaving South Dakota, I think I-15 from Salt Lake City south to Los Angeles would be a scenic drive.  That would take you by Zion National Park.  For all the places you are going, seven days is not enough time.  You might need to skip Texas.

You aren't going to have much time stop and look at anything. Driving time for your route, or for the best guess I can make of your proposed route, probably involves a minimum of 9 hours a day of driving, not counting traffic hold-ups, stopping for gas, food, or bathroom breaks.

There are so many things worth seeing that it's hard to tell what to suggest, even if we knew exactly where you'd be or what interests you.

I suggest googling, using the names of cities or states you'll be going through. They all have websites, usually more than one, telling about attractions of various kinds.