First, find a 5 star hotel ON or near the subway line (runs from the airport) AND is within blocks of the Forbidden City/Tianamen Square. Hotels are inexpensive in Beijing and the 5 star hotels actually have workout rooms with decent equipment. Chinese people do NOT exercise....so don't expect to find a workout room unless you go to a nice hotel. Download the subway map online and pick a hotel that you can get to by taking the subway from the airport. Cabs are cheap but traffic is horrible. You'll take a bus/tour to the Great Wall and one trip on their freeway system is enough for any visit to Beijing.
Three days there will be more than plenty
1 - run around Forbidden City, Tiananmen Sq, and go into the park next to the complex. The mornings in the parks there are very interesting. Everyone is out 'exercising' in a variety of different ways. It's a cultural experience. Get up early and run that area. Yes, it's horribly polluted. Did you not expect Beijing to be polluted? You just need to get over the air issues.
That same day, go do the walking tour at Forbidden City.
At night, make reservations for a Peking Duck dinner
2 - Take a tour out to the Great Wall. There is a combination Ming Tomb/Great Wall tour that is popular. Takes a full day but well worth it.
3 - Take a Houtongs tour of the old areas of Beijing. Fly out.
Stay away from street transport...use the subway. It's really easy to figure out and inexpensive. Don't expect anyone to help you find your way. The 5 star hotels will have English speaking staff to help you before you leave the hotel or if you want to make dinner reservations. TAKE THE HOTEL card with you wherever you go in the event you get lost....you can hand a cab driver the hotel card to get back to your hotel. Do not expect the cab drivers to know where they are going. They will not. Don't expect them to know street names, etc. They will most likely call the hotel and ask for directions if you're lost.
Some of the Olympic venues are still available to see but without events at them, they're not all that impressive. The Bird Cage is near the Hutongs so you can hit both of those on the same day......