How can I rent an apartment while unemployed?

I am currently looking to rent a studio apt for myself and my 3 yr old son. I am currently unemployed, yet still looking for work. I do side jobs to get extra money and I have a $2,000 savings account. My only source of income is public istance. I so desperately want to get a cheaper apartment than the 1 bd im paying for now, which is $600/mo. I also have plans to go to school in june 2010. I hope I can use some of that money towards rent. What should I or could I do?