The local Craigslist ads are my recommendaion.

FWIW, CGOAB has a "journal" of a guy who set out to "prove" you could ride a "Walmart special" on a cross-country bike tour. He almost made it then real life intervened. Point is, he rode nearly 2500 miles on the "special" loaded down with bike touring/camping gear before ending his tour/ride. AND he did it with no major mechanical failures. Who knows how much further the bike could have been ridden?

Buy what you can afford and take care of it.