Frank,
Sounds like you're going to North Hollywood/Burbank via Bob Hope airport. I've spent over 50 years of my live about 30 miles west of there in Simi Valley. For the most part, it's just a part of greater Los Angeles. I don't know what you're into, but if old pre-WWII airplanes is appealing I recommend a restaurant in Van Nuys called The 94th Aero Squadron.
Here's the link:
http://www.94thvannuys.comIt's not too far (by LOS ANGELES standards) from Burbank.
If you have kids, or young adults, there's Magic mountain to the north in Valencia. It's a Six Flags facility if you know what they're about. Very aggressive rides and some neat shows.
A few miles south is Universal Studios, that's a very popular spot with lots of great eats; bring your camera because of the excessive celebrity sightings.
Then there's the Hollywood Bowl. The schedule about now is mostly classical stuff with the L.A. Philharmonic. If you're not into it then don't bother. Summertime has a wider variety, but you need to know how to attend: It's a giant amphitheater and most will come with their picnic baskets - SERIOUSLY!
You can go online and get tickets to attend some shows. The Tonight show with Jay Leno is an example. They're free, but limited so you need to plan ahead . . .
The list goes on and on.
I've been to about 30 of the 50 United States, been to Europe and Asia, Canada and Mexico. As far as I'm concerned California has some of the best the world has to offer. Unfortunately, it has some of the worst as well. When you're in L.A. watch your step, don't go venturing into the wrong 'hoods (and don't wear RED - gangs take COLORS seriously).
Oh yea, the Channel Islands off Ventura has some of the best fishing in the world year round. Unfortunately with federal regulations fishing has been shut down until April.