DO NOT move to Simi Valley. It's a disgustingly hot white trash cesspool. I had to drop my buddies girlfriend off there 7 months ago and I still have a bad taste in my mouth. The thing that people think about when it comes to LA is that everything is a lot closer than it actually is. Granted, distance wise it may be, but the amount of traffic is UNGODLY. You'll find that where you live will really dictate how you live and what you'll do. When I first drove out here I crashed on my friend's futon in Little Armenia in Hollywood for 3 months which was cool for a while since it's close to all the sights like Hollywood Blvd, Griffith Park, Paramount Studios, etc etc. It was also cool because of how close other neighborhoods were, like Thai Town and Korea Town, and like dkn said Echo Park and Los Feliz which are the "cool" neighborhoods. And not that I really did it all that much, but downtown is relatively close, but unless you're going to a show or going to Little Tokyo, Chinatown, or getting drugs off of Skid Row, it's not really worth going down there. But even though I had access to all these places, I still pretty much just stayed in my Little Armenia bubble, since traffic is always a fucking nightmare.
After a month or so of moving out here I started dating a girl who lived on the West Side, and I ended up spending the majority of my time there. She lived just outside of Beverly Hills in a Jewish Neighborhood, and it was nice since it's a lot less hectic and trashy than Hollywood. Shortly after that I moved in with a couple of dudes I met through her in a neighborhood just east of Venice, and I love it. Rent's only $580, I'm 10 minutes from the beach and the Venice/Santa Monica boardwalk, and it's really mellow. But still, unless it's for work or to hang out with her or something, I rarely leave my area. So I guess what I'm blabbering on about is wherever you decide to move to will definitely dictate how you live and what you'll do. If you do decide to move to Simi Valley (shudder) or even the VALLEY valley (Burbank, Van Nuys) don't expect to be able/wanting/willing to go to all of the different parts of LA easily.
But, bottom line, FUCK Simi Valley.