You could spend the rest of your life just exploring Beijing. It is an ancient city of 22 million people. You aren't going to be coming to the end of it anytime soon. Unfortunately, you are probably on a limited schedule when you come to visit. Here are my picks as to the best highlights to maximize your use of time.
Essential Beijing Experiences
The Temple of Heaven
I think that the Temple of Heaven is one of the most beautiful places in Beijing and that the Hall of Good Harvest is a gorgeous building in the world. What you start to notice when you visit Beijing is how little about China you know. China's history is so rarely brought up in schools in the west even if you do massive amounts of reading and studying beforehand; you will be constantly amazed. There is the main track leading through the site but don't forget to peel off after or before to enjoy the gardens, pavilions, and the outlying buildings.
The Great Wall
You cannot come to Beijing-Especially as a first timer- and not go and see the wall. It is not optional and for excellent reasons. It is just that spectacular. You can improve your experience immensely with just a little planning of where and when to go. Do not just go to just any location. There are four main places to see the wall within a reasonable distance from Beijing's city center.
Badaling is far too close and crowded. All day every day. And the wall isn't somewhere that a crowd will enhance. This part of the wall is where most of the Chinese tour groups get taken. It is intense.
Mutianyu is slightly farther away. It tends to be where foreigners are told to go. Hotels have tour groups that come and because there is a bus from the city lots of backpackers. It is crowded, and I don't like how overly restored it is. The wall there feels a bit like a Disneyland version of the wall. Badaling has this same issue TBH. There is, however, a terrifying toboggan ride down if that is your sort of thing.
Jinshanling is okay. It isn't set up as well as the other places, but if you go during the week, the site isn't oppressively stuffed with your fellow humanity. There are way more stairs on the wall itself here, and the view isn't as good as in other places.
Simatai is my favorite. It isn't more than a few more minutes a total drive time than Jinshanling. It took two hours the last time I went there from Sanlitun, but it has taken as much as four and a half depending on traffic. There is a Watertown at the base of the mountain. It is completely fake and made for the tourists, but it is brand new and clean. It is again a Disneyfied version of China. my father enjoyed it when he came to visit. It takes about an hour to walk through to the lifts up to the wall itself. You can, however, choose to completely bypass it and take a shuttle bus to the cable cars. If you go during the week, you can be lucky and have the wall completely to yourself. I think that the view from Simatai is the best as the mountain falls away from the wall itself dramatically. There used to be a hike that you could take from Simatai to Jinshanling, but I have been there four times, and the wall has never been open in that direction. If you are super into hiking, I would suggest looking into the parts of the wall that are not restored. TL/DR- Weekday Simatai is your best bet. Ignore the fact that there is a woman next to you dressed in a ballgown and wear clothes you are comfortable hiking in.
This is an art district and the center of Chinese hipsterdom. It is one of those places that is improved by the bustling crowd so plan on going on the weekend. There are endless galleries, art "museums", art exhibitions, shops, and restaurants (the coffee is good but none of the food has impressed me yet).
The Summer Palace
One of my favorite places in Beijing. It is beautiful even in the winter but at it's most spectacular in April. Definitely, go on a weekday. It is a whole day affair. Spring for the audio guide. When they are offered, they are quite worth it. Do yourself a favor and wear comfortable shoes
Houhai Lake and NLGX
Do you like crowds? Let me tell you that there is nowhere on earth better for people watching than China. This is an outing better done on the weekend. If you walk around the lake and then swing around to NLGX a gentrified and commercialized houtong nearby you will see modern Beijing at it's most authentic. My favorite shops are Plastered 8, which has really cool Beijing t-shirts and merchandise and the store that makes jewelry out of ancient broken porcelain (beware: it is very very expensive, and you will want it all)
Drum and Bell Towers
This is the Chinese equivalent of a clock tower. You might not think that you are interested in historical Chinese methods of keeping time but you would be wrong, my friend. The view alone is worth it. Warning: if you can't do stairs then this is not a place you want to waste your time on. Both towers have very steep six-story staircases (without a break) Make sure that you go on a clear day and that you stay for the regular drum show.
Make sure that you go on a clear day and that you stay for the regular drum show.
The Forbidden City/ Tiananmen Square
This is a whole day thing. Really. You are going to be here all day. Accept it. There is so much to see. Tiananmen Square doesn't take that long. Maybe an hour. Has anyone been to the sunrise flag raising? I have lived here for three years and have not been to it yet. Is it worth it? If you can figure it out (it isn't that difficult, honestly) take the subway.
Taxis can't drop you off in front of the city, and you will be wandering for awhile. How is possible to lose a city?! Not that that has ever happened to me. At all. Get the through pass. Actually, if there is an option for a through pass anywhere in Beijing get it. It isn't that much more, and it will save you SO much hassle and get you in some of the hidden places of the city. In the Forbidden City, the Hall of Clocks is particularly impressive. Be prepared to mix up your dynasties. If you wanted to extend your day you can visit Mao's Mausoleum in the center of the Square and the park across the street of the exit of the Forbidden City. If you clim to the Pagoda on the hill in the park you get an unparralled view of the scope of the city and the square.
I think that there might be a couple but I have always gone to the one at the Chaoyang Theater in the Central Business District. There are several performances a day and the tickets are easily bought on line through the website or through trip advisor. The tickets aren't as cheap as you might expect. About 40$ a person for an hour show. But holy crap your mind is going to be blown. Think of Cirque du Solei. Then amp that up to 11. If acrobatics has a box, then this group laughs at it and then uses that box to juggle motorcycles. The first four rows are cheaper and worth getting.
Things that you could skip:
The Olympic Park: It is huge, kind of empty and honestly a little depressing since the stadiums fell into disrepair almost immediately.
Prince Gong's Mansion: If you have seen the Forbidden City and The Temple of Heaven the palace doesn't have much more to offer and it is always FULL OF PEOPLE. I think that it is on a tourist route, but there is just not enough room for everyone
The CBD: Drive through it once. There are the buildings. Yes, super impressive. Job done.