The Great Wall
No trip to China is complete without seeing the Great Wall. Fascinating the world's imagination since long before the rumors of it being the only man-made object visible from space, the Great Wall was one of the ancient world's greatest engineering triumphs.
How you want to see it is up to you. Depending on your budget and your time, there are many ways to view the undulating fortification meant to protect China's northern border and regulate Silk Road trade.
Budget friendly options from Beijing can be arranged for a handful of dollars via public transport, though this will only get you to Badaling, the busiest section of the wall, though this is also were the Great Wall Museum is located.
Group tours will take you farther for relatively cheap, though the cost of keeping the price down is visiting jade and tea shops along the way. These tours will usually get you as far as Mutianyu, which is far less crowded than Badaling, making the extra money and wasted time at trinket shops well worth it.
Arranging a private taxi from Beijing is more expensive, but allows you to skip the trinket shops, and will give you the freedom to venture out to Gubeikou, Jinshianling, or beyond, where you'll see the wall in a slightly less polished manner.