+1 on the warmshowers recommendation. A student of mine did a 400 mile tour last summer on a racing bike. He did the whole trip only carrying a couple of water bottles and one small bag. He stayed with people he contacted through warmshowers and told me it worked out great. He just bought food and drinks along the way.
I disagree with the suggestions of modifying an old mountain bike or your existing road bike to make it into a tourer. You do that sort of thing if you have money, love the bike frame, and enjoy being a bike mechanic. It won't end up saving you anything. In the end, you are better off buying the $600 Windsor Tourist if you really want a bike capable of hauling a load.
For example, if you upgrade to 36 spoke wheels, that will cost you ~$250. A new cassette with bigger gears is ~$30 at least, you'll probably need wider tires to go with the wheels (~$60 for two), might need new tubes to go with the tires (~$15 for two). Oh, then you probably need a long cage rear derailleur to go with the new cassette (~$60). If you decide to install a triple ring crankset to give lower gearing, it will be around $120. You'll probably then need a new bottom bracket (~$30) and front derailleur (~$30) to go with the new crankset. I could go on, but you get the point. The parts I just listed cost around $600 and doesn't include the cost of tools or hiring someone to install them. Even if you did all of what I just said, you are still left with a frame that probably doesn't have braze ons for mounting racks, and probably doesn't have a long chainstay so your heal will be hitting bags carried on a rear rack.