I'll second the suggestion in the askme thread of the Museum of Jurassic Technology.
You should also go to Randy's Donuts or Kindle's Donuts and get a "big donut"--especially if you have someone to share it with. They are embarrassingly big to eat alone.

I'll keep talking.
Ok, so near LACMA there are lots of really good soft tofu korean places that are cheap and you should definitely try.
You should also have a burrito from one of the food trucks in the area.

A little farther away, the Norton Simon museum is a great, small collection that is the perfect size for a short visit.

especially if you have someone to share it with

I'm actually flying solo, which is my least favorite way to travel. I find myself less adventurous unless I have someone with me. But I'm committed to making the most of my trip. The friend I was supposed to stay with who was going to shepherd me around the city flaked out last night--three weeks before my visit--so I'm scrambling to make plans. I appreciate sincerely all the help I can get.

Aw that's a shame. Well, you should still go eat a big donut, or you can get a regular sized one. But it's neat to see the storefront, because once you do, you'll notice it in a ton of movies and images.
LA isn't a bad place to visit alone. Most people are alone in their cars anyway, and you can go everywhere you want to since no one will complain about your choices or bore you with theirs!

I do recommend the drive up to the Norton Simon- aside from seeing cool art once you're there, the drive itself takes you out of the valley and into the hills, which can be a nice change and the hills will be all green and pretty when you go. You get to see a little more of the natural topography. Pasadena is a cute little town with some good thai food, too.

For entertainment, I see you want to go to a UCB show. If you like it (or even if you don't) you might want to check out a Groundlings show as well. LA is their stronghold, while UCB is more NY with a kindo f secondary group in LA.

I've recommended the Museum of Jurassic Technology to people and immediately smirked to myself, thinking, "Yeah, but that person just won't get it."

You, ColdChef, will GET it, and you should make it a priority.

The Museum of Tolerance, followed by a meal at Canter's makes for a nice day.

A Dodger game, a visit to the beach, although, as you can see, we are into the "June Gloom" phase, right by the ocean.

Tito's Tacos is a regular stop for me, when I am down there, also.

Dude, Hollywood Forever Cemetery . For obvious reasons.

For a taste of OLD LA. . .The Pantry is interesting, if only for it's longevity. But it's what downtown used to be like.

Forget LA and drive to Tijuana. (Hey, I'm just being honest here.)

Thanks for the advice, folks. Keep it coming. I'm quickly discovering that I haven't allotted enough time to see and do and EAT the things I want to.

I can't read the AskMe, since work has decided that anything but WebMD and CNN is worthy of blocking (oh, and mechat).

As a former Angelino, I can weigh in on some of the more unusual tourist destinations for people on a budget:

The Temple of Self-Realization is beautiful and a fun little side trip if you are going down PCH to the beach.

Oki-Dog is the most wonderful and nasty concoction ever, and should be sampled once in a lifetime.

If you are into gothy dead things (taxidermy, etc), Necromance on Melrose is fun if you are in the Melrose area.

Pink's is a legendary hot dog stand, but IMHO the food isn't that great.

If you are into gothy dead things (taxidermy, etc), Necromance on Melrose is fun if you are in the Melrose area.

OMG. Necromance just went to the top of my list. Awesome.