@Apple fanboy, I'm STOKED that you get to visit LA! Your first vacation in a while you say? You're going to have a terrific time.
I assume the exhibition is going to be at the LA Convention Center, which is downtown. The beach is a decent distance from downtown (factoring in traffic), so that's something to consider if you're planning on going there in the evenings (with no traffic, you can get from downtown to the beach in ~20 minutes).
If you're wanting to get some killer pictures, you have to visit the Griffith Observatory at sunset. Better yet, if you can get some shots of the city as the lights begin to come on, you're golden. Definitely make that a stop:
https://goo.gl/maps/n3Zd6NAwr9R2
Here is another terrific view, the Jerome C. Daniel Overlook (I haven't done this one! Post pics if you do!
):
https://goo.gl/maps/e6orQ5j3APo
^You might be noticing a theme -- the mountains that look over the city are some of the best spots for photos.
The northern section of downtown -- the area near City Hall -- is really beautiful. A great spot for photos is the Los Angeles Department of Water and Power. There is a big pool that encircles the entire building. You can get some cool shots of the LA skyline from here:
https://goo.gl/maps/2iRr57PaaKR2
Echo Park might be a cool stop as well. However I'd try and go before it gets too dark out:
https://goo.gl/maps/coZif8RoRYt
The Hollywood sign is really cool to see since it's so iconic, but it's one of those things where, once you see it, you go, "Oh, that's it?"
-- Everything listed above is close to downtown. If I were you, I'd try and knock out those during the days you have the exhibition going on. I'd save the beach for Friday, when you have a full day. Now, speaking of the beach...
Venice Beach is really cool. Very iconic. Great chance to get pictures of folks playing basketball, folks working out, folks skateboarding, or the lifeguard huts along the beach. Cool place, very populated during the daytime. Wouldn't recommend being here when the sun goes down, though. Hotel Erwin has a cool rooftop bar.
Santa Monica is a beautiful part of town.Just up the road from Venice Beach. Check out the Third Street Promenade (you can't miss it -- all of 3rd Street is foot traffic only). Then walk to the Santa Monica Pier and get pictures of the Ferris Wheel. I'd recommending visiting Santa Monica during the evening since the Ferris Wheel lights up. And you can't beat the sunsets here, believe me.
Two last things: You HAVE to try In-N-Out Burger. Get some animal fries (if you're not allergic to cheese or onions). Trust me. And you have to try Blue Bottle Coffee. If you're a coffee snob like me you'll love it. Both In-N-Out and Blue Bottle have locations around LA.
If you have any more questions at all, feel free to reach out. Heck, send me a direct message if needed. If I lived in LA, I'd say that we could hang out. Alas, I don't (yet!). Have fun, friend!