Good advice offered already.

If you have 1.5 days, assuming one of them is not a Monday, I suggest GW in the early morning with a private driver: avoid Badaling if possible since it's too crowded -- Mutianyu is a decent compromise choice: it's restored, not _as_ crowded and has the novelty option of a toboggan ride on the way down. In the afternoon, just check out Tian'an'men, Wangfujing etc, or if no smog, Jingshan park just before sunset for a spectacular view of the Forbidden City. Forbidden City itself can be "done" in about 2-3 hours so can leave to the 'half day" assuming it's a morning. There is a cap to the number of visitors, so arriving in the afternoon can mean tickets are sold out...

Alternatively, if flight back is mid to late afternoon, could go to Mutianyu upon check-out of hotel early morning, and then straight to the airport, since Mutianyu is sort-of that side of town. Drivers are pretty honest and reliable. The drive to Mutianyu from centre of town takes from 70-120 minutes depending on traffic (assuming you are not arriving during QingMing, when those travel times could double).

tb