When you say "move to LA", you're talking about a 4,000 square mile metropolis made up of hundreds of cities. Technically I live within the city of Los Angeles, but in a completely separate town, in a different valley over the mountains, 30 miles from downtown proper where your mailing address is actually "Los Angeles". I would not live anywhere near that place personally but a lot of people love it.
There is a lot to consider, both good and bad. As a major city, Chicago is FAR nicer than Los Angeles. But LA doesn't really have a downtown in the traditional sense like many other major cities. It has more of a civic center, and the city itself is spread out over a huge area. Whatever you're looking for, you can find it here if you search hard enough. But be warned, a lot of other people want what you want in a lifestyle, and the cost of living will represent that. Living in some of the beach communities, you will pay dearly in rent and they are very crowded, fast-paced places to deal with. But you're also by the beach, often surrounded by great cars, food, etc. so for some the pros outweigh the cons.
I work in TV and film so much of my days are spent in Hollywood, Burbank and Culver City. Working in these busy areas are more than enough for me, and I'm always happy to return to my quiet neighborhood. Some people work and live in these areas and love it. Me, I prefer the 45-90 minute commute so I can live "on the edge" as I like to call it. In ten minutes time, I can be driving mountain roads surrounded by pine trees.
If you do move here, spend some time traveling around to find the right area. Don't settle on the first nice place you see! You can live at the base of the 11,000-foot San Gabriel Mountains. You can live by the beach, or live the nightlife in the city. You can live in the suburbs, close to ski areas, or even out towards the Mojave Desert for off-roading. It's all within 100 miles of each other. And no matter where you go, there are always interesting cars to be found.
Let me know if I can be of help!