One way to travel and really see the culture of a country is to live there and work. Teaching English is one popular way to do this. You get to interact with people for a longer period of time in everyday situations and make long lasting friendships.
During your time off, you can travel around and see other parts of the country.
You might not make as much money as in your own country, but it probably means you won't be spending as much either. You might reduce your money saving power, meaning options like buying a house back in your country would be more difficult if/when you return to live there. This is a trade off with the life experiences you gain.
ESL Cafe - provides resources and listing for teaching jobs in Asia.