I'd recommend giving
priceline.com a try. Set your preference to 4-5 stars (all the downtown ones are in that category, so you should end up downtown). Then set your price and hope for the best. :)
Also, check the bus routes--if you don't want to rent a car--or discuss more here to find others to car pool with.
We'll get a "Travel" wiki page up--folks tend to add the plans there, so they can "collaborate" on getting around cheaply.
Laters,
Benjamin