JDG,

Don't be so quickly discouraged. I was more or less in your boat about a year ago and now here I am settled in Mexico with an apartment and a job. It is very doable. I don't have any suggestions on locations as I am in a large, polluted city -Monterrey, but I love it nonetheless. The tourist visa is fairly easy to get. I'd suggest travelling at a slow pace until you find a place you like. It is very affordable here if you are good at living within your means. When you find a place you like, you should be able to find a job teaching English in any decent size city fairly easily as a native-speaker, especially if you have a degree.
Definitely let me know if I can be of more help. I think it's a great idea to get away and this is a great place to do it.