The mathematics of a cheap used car can be very favorable vs. renting, IF done correctly. Three years ago I moved from Europe back to the states and was renting a lot. I ended up just buying a $2400 '98 accord (which had a great engine but had clearly been in a low-speed accident with a big dent), using it off and on, and selling it 2 years later for $1800. It was particularly awesome because since it already had body damage, I could get the cheapest liability-only insurance available and not worry about anything happening to it. (I can't tell you how much fun it is to not let people cut you off because your car is nowhere near as valuable as theirs :) )
I have 2 recommendations. First, your price range is too high. You want to buy something very cheap for whatever reason (older model, etc.) but which runs really well. When you go to resell it, it will get approximately the same price as when you bought it since it the equation is still running engine + undesirable car = baseline value. If you buy something in the $7-8k range, you'll eat a few thousand in depreciation whenever you sell it. Second, get the bare minimum of insurance and self-insure with the idea that damage to your beater isn't worth fixing.
Or third, just bike over to the zipcar and throw the bike in the trunk! It's only 6 miles.