which is the nearest great China wall from there,the distance and the mode of public transport?

It should be Badaling section. The distance is around 60 kilometers. You can walk to the People's Univesity Subway Station from your hotel. There you can take subway line 4 and get out of the Exit C. Then you can walk around 140 meters to find Ping An Li Lu Kou Bei Station. There you can take T13 to reach Deshengmen. From Deshengmen, you can take bus no. 919 or 877 to reach the wall.