Travel plan help!

Hi all! I will be travelling to China with a friend for 1 month (I have citizenship, but my friend is a foreigner, and wants to stay for the maximum duration for visa-free entry, which is 1 month). I am wondering how we will fill out time? Both big time history geeks, and also want to have fun and do non-history related stuff. I've toured China before, but only when I was really young, so no I am going with a new perspective, and he is a first-time visitor. We have planned to go to Hongkong, Shenzhen, Xian and Beijing, but not sure what to do/how much time for each place. We want to visit al of the historical places in mainland (Forbidden City, Summer Palace, Tiananmen, the various Beijing, Xian museums, Terracotta Warriors, and especially hutongs and traditional, old-town style streets for shopping and exploration etc. (For Hongkong, he can enter visa-free and I have already procured an unlimited entry pass. For Shenzhen, we have a relative's empty flat to stay in, which is also close to the border of Hongkong, so we are conflicted as to whether stay in Hongkong accommodation or traverse the Shenzhen border each day)

Keep in mind, we are planning on budgeting, as in no fancy hotels or resorts.

Any help is appreciated, and please ask follow up questions if need clarification. Thanks!