Looking back at my calendar, it seems I went to Peking Man Site
on the Saturday (also in October) it certainly wasn't very busy when I visited. And the Metro line extensions should make it an easier place to visit now.
Just looking at it on Google Maps Satellite view
(NB it is always out of sync with the street map in China) it seems there is a giant canopy being built over the whole place so I'm not sure if that may restrict access.
Also perhaps a trip out to the Grand Canal
at Baliqiao which may would also avoid the crowds, though you can also get a tick by going to the much more central Shichahai
, just behind the forbidden city.
I was trying to engineer it so I wasn't in a big touristy place over the weekend, but I visited the Forbidden City on Sunday
, and except at the tighter more confined bits at the end, the crowds were very manageable.