How can I go to Great wall from Beijing Marriott city wall hotel at 22 or 23 July 2013?

Sorry this is too late you. Anyway, it could be expensive to take a direct to reach directly. And which section will you visit?

Badaling section: As your hotel is around 2min walking distance from Jianguomen MTR Station, you can take local subway line 2 at that station to Jishuitan Station. Walk from Jishuitan to Deshengmen to take bus no. 919 or 880 to Badaling directly. The MTR fare is CNY2 per person and bus fare is CNY12 per person.

Mutianyu section: It is suggested to take a taxi to Dongzhimen Outer, where you can take bus no. 867 to reach there directly. The taxi fare is around CNY15 and bus fare is CNY16 per person.