I hope you are having a great time and this message isn't too late, I only have experience of Beijing but maybe this would be of us for a WHS spotter.
Aside from the obvious and those already recommended there is the outlying WHS of Peking Man, some details of getting there under your own steam can be found here
. It isn't astounding so if you are short on time it is one to skip, but it is kind of fun just getting there, and it is an important site.
There is also the chance to get a look at the proposal being put forward next year, the terminus of the Grand Canal is only about 35 mins from central Beijing. Hop on Metro 1 (I think you technically have to change onto BT line but it is basically a continuation of line 1) and get off at Tongzhou Beiyuan
. There are a few buses that then run along to the canal (including the 12 & 19 I think). It isn't the most wonderful sight in the world but you can see a potential new inscription and get off the Beijing Tourist trail for a bit. I think it took me about 3 hours for the round trip from Tienanmen Square, on the metro keep an eye out for the wonderful Ming era bridge at Baliqiao
If you do go to the Drum and Bell towers I found some nice bars nearby and enjoyed an evening beer whilst watching the locals on the square mass ballroom dancing, it was very enjoyable.