Considering Beijing is so large and is chock full of such history and culture, it would be difficult to pick one single highlight. Choosing between Tiananmen Square, the Forbidden City, the Summer Palace, and the rustic old Hutong areas is almost impossible since each has its own charm and wonder. If I am forced to choose though, I would go for the Summer Palace. Even though it is an hours bus ride from the center of the city, it is well worth the trip. The palace and accompanying temples is sat on a hillside on the banks of Kunming Lake. In winter you can walk out onto the ice to enjoy the view; or equally beautifully in summer, you can take a boat ride to admire the view.
Quick Tips:
As always in big cities, be careful. China may be Communist in name, but the capital city is rammed with people exceptionally keen to make an extra buck, or yuan in this case. Almost no prices for clothing, electrical goods, or souvenirs are fixed, so barter hard. Don't be afraid to sound ridiculous when you offer a price to a Chinese person who is selling something. They are probably marking it up by something like a thousand percent at the start.
Best Way To Get Around:
For a city of its size, Beijing is served poorly in terms of its subway. There are only three lines which, even though they are cheap (around 40¢ anywhere), leave massive areas of the city untouched. If you are venturing away from Tiananmen Square and the central districts, other options are needed. Cabs are relatively cheap and exceptionally plentiful. Buses are cheap and frequent, but finding out which one leads where is a struggle at the best of times.
The Kate Melu song may say that there are nine million bicycles in Beijing. But anyone who gets on one to go more than a few hundred yards takes their lives into their hands. The Chinese drive like maniacs, meaning the city's larger roads are no place for a gentle bike ride.