If you want free, just google "boondocking". It's the RV term for a free stay.
If you want a little more safety and amenities than the Walmart parking lot, try a campground. They are much cheaper than hotels, they will have bathrooms and showers for you, and you can reserve 'em ahead of time instead of looking for that place to stay late at night.
I use them to split up long drives. Just be aware that they aren't hotels, so if you are planning a late night arrival, let them know ahead of time. Some places can check you in late at night, and some can't. If your contest is on a holiday weekend, you will need to reserve well ahead of time, and might have trouble getting a single night stay.
www.koa.com has a network of sites, and online reservations. There are lots of other places out there that will be cheaper, but you might have to go old school and use the phone to reserve. (the horror!
) National Parks are especially cost effective, but sell out early.