There are public school jobs available in China's backwaters for you and other non-native speakers of English as well as old laowai of pensionable age who are native speakers. The agent I work for employs Africans and East Europeans too. What I like about working for him is that he's honest and provides me with a teaching assistant. She definitely makes my job easier and helps me with my daily life problems outside the classroom.
Wherever you end up, have a good time, and never ever take a job at a private school, especially not at a training centre/language mill set-up. Many newbies have been burned badly after they were enticed there by high salaries - either the high salaries were a fabrication, or the foreign teachers burned themselves out teaching far too many classes/week to get the big money!
Surf the web for Yuncheng jobs, but if you choose to apply to an agent in that area, make sure you do so direct, and not through a recruiter. Recruiters supplying Yuncheng's agents with foreign teachers will demand introduction fees from the agents. I think that would have a detrimental effect on your employment package, as the agent will recoup that expense by paying you less salary/month, or less air fare reimbursement when your contract's up!

I have a couple of suggestions for you. Given that you're not averse to teaching off the beaten track in China, and you have no teaching experience, I think it would be a good idea for you to apply to agents rather than to recruiters. You would be teaching for the agent. He would place you in a middle school, and supply a Chinese teaching assistant. He (or she) would teach you how to teach, as it were, as well as make it easier for the students to follow your lessons. I think this would be a good way for a non-teacher to start teaching in China. Last year around this time I bumped into a Spaniard teaching English for an agent in a county. His name was Javier, and I'd say his English was pretty poor, but he was managing to satisfy the middle school where he had been placed, and consequently, the agent who had placed him there. His teaching assistant must have been able to ensure his continued employment by helping him plan his lessons well. The only complaint he had was that teaching each lesson over and over again during each week, week by week, was boring, but he did say he was able to amend it as he went along, so as to improve it.
I know agents and Chinese teaching assistants are criticized severely here by some posters. So, I think it wouldn't be a good idea for me to name said agent on here. But if you like you can e-mail me and I'll tell you how to contact said agent. Anyone else interested, please feel free to do so.