You mentioned Hwy 1 so I imagine that will be a drive on the PCH through Big Sur; truly stunning. Spend the night at
Pfeiffer Big Sur SP if you can.
Since you'll be in Vegas anyway, take the time to visit
The National Atomic Testing Museum and the NTSHF - Las Vegas, NV, it's a truly unique museum dedicated to a truly surreal period in American history. Also, Hoover Dam is only a short drive from Vegas. On the way to Vegas from LA, just off the 15, is "Calico Ghost Town", a throwback to kitschy 50's tourist traps except it's actually very cool and won't take up a great deal of time. After Calico you'll be hungry so stop in at "The Mad Greek" a few miles down the road in Baker.
While in LA, and as tempting as the famous freak show at Venice Beach is, check out nearby Abbot Kinney instead. If you're interested in a time capsule of the Southern California beach vibe, take the scenic route to Vegas and visit San Clemente and Doheny Beach of The Beach Boys fame. It's south of LA on I-5 and when you're ready for Vegas you can take the 74 through the Santa Ana Mountains and hop on the 15. BTW the best burgers in Southern California are at the end of the exit ramp for Doheny Beach, "A's Burgers". The Double A with cheese and some onion rings will be just the ticket to start you on your way to Vegas.
Have fun.
PM me if you want meet up when you're in LA. If I'm not working I'm game.