Great Wall of China
The Great Wall of China is certainly China's most famous landmark and one of the most famous man made attractions in the world. It starts from the Liaoning Province and travels through Hebei Province, Tianjin Municipality, Beijing Municipality, Inner Mongolia Autonomous Region, Shanxi Province, Shaanxi Province, and Ningxia Autonomous Region to Gansu Province.
You certainly do not have to see the entire wall, in fact it would be very difficult to do so as it is a few thousands kilometers long, but you can visit it at a number of places. Some places are easy to access whilst others are very difficult and require some skill.
If you are starting from Beijing then you'll be able to see many of the popular sections of the wall within one day. Badaling and Juyongguan, being closest to Beijing, are the busiest locations but worth visiting if its all you have time for.
Alternatively if you want to go somewhere less crowded then try Mutianyu which is still near Beijing. You can use a ski lift to get on the wall or hike up the steps.
Further away (80km) from Beijing are Gubeikou, Jinshanling and Simatai. It is worth going to any of these locations as there are less people. There are also minimal commercial vendors in the area so bring your own food and drink supplies.
Some people like to hike the entire Great Wall in which case you'll have many points of interest to stop off at including Wuwei, Minqin, Zhangye, Jiayuguan and Lanzhou which is a former walled town.
In Ningxia you'll come across the Eastern, Northern and Western Ningxia Walls. The Eastern Wall contains Hongshan Castle and Water Cave Gully which are spectacular points of interest.
The Great Wall of China is a wonderful spectacle regardless of where you see it and how much you see of it. You’ll feel satisfied knowing you have personally seen one of the greatest feats of human construction.