How to make the most of internship housing stipend?

I will be interning at a well-known company in Seattle this summer. I get to choose either subsidized housing (I pay $300-800/mo) or receive a couple thousand per month to find my own place. Clearly the second option is better for my take-home pay if I don't spend it all on rent, so my question is how do I make the most of it? Where do I look, what do I look for, and how much should I expect to spend? The first option is obviously easier since I don't have to find it myself, but if I can save some money without too much trouble then I'd like to.