You can see the Great Wall at Yellow Pass, which is within the Tianjin Municipality. It about 2 hours to the north of the city and far less crowded that Badaling in Beijing. You can do a day tour from tianjin city quite easily. I suggest you take the bullet train early one morning to Beijing. Take taxi/subway to Tiannanmen Square. Look around here, see the Mao Zedong memorial (view Mao's preserved body), go over the road to the Forbiddon city and spend the rest oif the day looking around the shops area nearby.i.e. the central part.
Another day you can go to the Summer Palace and look over the Olympic Stadium. Note trains go till about 11pm at night. Enjoy some great restaurants in Beijing.