Cheapest short-term Housing in the LA area?

I'm planning on a trip to California at the end of September and haven't had much luck in finding affordable, short-term housing. See I'm not so sure if I want to live there permenatly, this will be a sort of test run to see if California and I agree. I have been searching for a short term residence, with possible roommates but it's not mandatory. I need a place that will let me stay for about a month, which should give me ample time to make a decision and should I decide to stay to find a place to live. I have a very limited savings, and would be able to spend no more than 600 for the months rent. I will be flying in to LAX and not have a car, so I will need to be located close to town, if not in it. I will probably get myself a bike to use while there. I love to get fresh food from the farmer's market, love exporing different cultures and I am a vegetarian, so vegetarian restauraunts would be great, but not mandatory. Any help or advice would be greatly appritiated. As would any tips on how to live in the LA area on a resitricted budget.