The first thing you should know is that it's been over 80 degrees the last 2 days...and it's almost Thanksgiving.
Your first $20 should be spent on a Zagat's guide. And then check out all the "best buy" restuarants. Lots of great food at reasonable prices.
I spent most of my 20's in L.A. Before moving a little bit south. Wouldn't trade it for anything. You really get a sense that there is lot's of opportunity and anything is possible.
Relationships are hard in L.A., everyone is there for some other purpose that usually trumps relationships. The late Sam Kennison called L.A. "the land of wounded bitches". You'll see what he meant.
What are your details? Age, job and marital status, etc? That makes a difference in where you want to live and what you want to do.