There is a direct bus running from Tianjin Airport to Beijing. If you want to experience the bullet, please take airport shuttle bus to Tianjin railway station first, and then change to the train to Beijing (Don’t worry. You need to take airport shuttle bus at Gate 2 of Domestic Exit. If you can not find it, you may ask the staff in the airport.)
There are many scenic spot/region in Beijing, The Forbidden City, or Summer Palace are in downtown Beijing, you may reach there,by metro or bus, Badaling Great Wall is also famous spots, it’s a little far from downtown, anyway it’s easy to get there, there are shuttle bus No. 919 to get Badaling Great Wall (See here the )
For the shopping in Beijing, Xidan, Wangfujing, Xiu shui and the wholesale market around Beijing zoo. You may take get there by both subway or bus.