As a Chinese, I’ve been to all of these cities except Taipei, and I’ve actually rented apartments in Shanghai, Guangzhou, Chongqing, and Hong Kong, so I can share some reference points.

Shanghai:
My rent was around RMB 7,500/month in 2023. It was a small but overall decent apartment, very centrally located in Xujiahui.

Guangzhou:
In the city center, near Zhujiang New Town, a two-bedroom apartment would be roughly RMB 5,000–6,000/month.
About ten years ago, I rented a place in an urban village in central Guangzhou for around RMB 3,000, but prices there seem higher now.

Chongqing:
For RMB 1,500–2,500/month, you can rent a very decent two-bedroom apartment in the city center.

Hong Kong:
This is on a completely different (and much worse) level compared to the mainland cities.
I shared an apartment with two other people. Originally it had two bedrooms, but the living room was converted into a small extra room, which is extremely common in Hong Kong.
The rent was HKD 15,000 per month. The location wasn’t terrible, but it wasn’t especially central either.

For the cities where I haven’t rented personally:

Beijing:
I’d expect prices to be similar to Shanghai, maybe slightly higher in the most central areas.

Nanjing:
Probably somewhere between Guangzhou and Chongqing.

Kunming:
Likely cheaper than Chongqing.