For travel over the 4th of July holiday, fly nonstop from Los Angeles to Austin for $183 roundtrip on American.
I found flights departing Los Angeles LAX on Tuesday, July 2, returning from Austin AUS on Friday, July 5.
You'll find lower fares available for non-holiday travel.
This fare includes a carry-on bag plus a small personal item. The first checked bag costs $30 each way.
Seats will be assigned at random after check-in for this Basic Economy fare.
A Main Cabin Economy fare is $253 roundtrip, which includes advanced seat assignments and allows upgrades/ticket changes (fee applies). A checked bag is the same $30 fee each way.
Note, that the selected flights require an early 6:00 am departure on July 5. If you'd like to leave later in the day or the following day, it is nearly $100 more. More reasonable flight times are available for $280 roundtrip in Basic Economy or $310 in Main Cabin.
Need a room in Austin? Here's what's available for the Fourth of July dates on Hotelwatchdog.