If I am only traveling Beijing for 3 days (72 hrs), and I want to see the Great Wall,do I need visa?

I am traveling from South Korea. I know Great Wall may be outside of City limits so wanted to know if it is possible with the free transit stamp. I have a United States passport. It seems rather steep to pay $140 usd to see the Great Wall and Beijing in that 72 hour time frame but I rather be safe and make sure first.