The local newspaper here has a section in the classified for anything under $500. Sometimes there are cars for sale there. Look in the advertising magazines that you can buy in convenience stores for about $1.50 or sometimes they're free. Bulletin boards in grocery stores, churches, the barber shop.
Odd that this should come up now - I'm looking for just such a car for the 3.4 mile commute to the job that I started last month. I'm driving a full-size 4WD pickup truck that I bought new, is now six years old, and that short of a trip made repeatedly is terrible for it since the engine never gets fully warmed up. I often take the "long way" home but that's still not enough. So I'm looking for a "beater car" that I don't care what it looks like as long as it's safe and runs. Doesn't even need A/C or a radio. I figure that if I buy a car for $1,000 or less, insure it for liability only, and it runs for two years I got my nickel's worth.