how far is it from the airport to the Great Wall?

I donot recommend you go in a tour. Many of the tours will cover some other attraction sites and leave less time for Great Wall travel.
From the airport, you can take airport express and then subway to Jishuitan and walk to Deshengmen to take bus no.919 to Badaling if there will be less traffic jams then.
If the traffic jams still happen a lot by then, you can take the subway to Xizhimen, then walk to Beijing north railway station to take a train(Y567 at 09:33 and Y575 at 13:19) to Badaling.
You can go back to Beijing downtown area the same day either by bus no.919 or train.

Thanks a lot Mr.Chang :)