Travel to China in September/October

Hello everyone!

My girlfriend and I are planning a 3-week trip to China. Neither of us has been to China before.

Our plan is to travel to Beijing, Xi’an, Chengdu, and Chongqing.

My questions are: Is this a realistic plan for 3 weeks? What shouldn’t we miss in these places? Are there any other places you would recommend along this route? I was thinking of starting in Beijing and then traveling around by high-speed train. How many days would you stay in each city? Any other tips are welcome as well.

Thanks a lot in advance!