https://www.princeton.edu/~ota/disk1/1989/8926/892606.PDF
A decent source as any. A city in Antarctica would pretty much be mining and tourism. Anything much bigger than 10,000 seems a bit unrealistic for the near future, although in a worst-case scenario for Earth, where
global warming exceeds our worst fears and we can't get anything going in space, colonising Antarctica will definitely take place and you'll probably see some sizable communities form.
Ideas would be:
Antarctic Peninsula--It's relatively ice free and has comfortable weather by Antarctic standards, plus no/minimal polar nights. It also is geologically associated with the Andes, and it is strongly believed that some of the world's richest deposits of copper are in those mountains. These are linked to large molybdenum deposits, a lot of lead, tin, and zinc too, as well as most enticingly, gold and silver. Let's say there's some initial prospecting, and someone finds an Antarctic equivalent of Cerro Rico, the mountain of Potosi. In the surrounding area (within a few hours distance), there's some other incredible strikes of gold and silver alongside mountains of copper. And at the same time, let's have Chile, Bolivia, and Peru be gripped by some massive chaos, causing their mining production to drop. It's worth throwing in South Africa having severe problems too to further wreck world prices. Obviously the best pick.
"Coast" of the Weddell Sea nearest Pensacola Mountains--The Pensacola Mountains are probably some of the richest on Earth in terms of resources, akin to the great finds of gold and especially platinum group metals in South Africa, and alongside it, chromium, copper, and uranium. The main problem is the mountains are well inland and locked by a huge ice shelf from which massive city-sized icebergs frequently break off from. The Weddell Sea also has some of the most awful conditions of any sea on the planet. On the bright side, the Weddell Sea likely has some of Antarctica's best offshore oil deposits. This would be my number two pick--collapse South Africa and the Andean states and why not the Middle East too, and with the right finds you might get something working.
The East Antarctic Shield, much like other very old formations in Australia, Canada, and South Africa, is also highly likely to have some incredible finds. Somewhere, if you have a few nearby (within a few hours distance) clusters of incredible finds, like a few high-quality rare-earth deposits, huge gold mines, etc., then you might be able to develop a port city in the area.
The problem in all this is mining it profitably. In theory, it's probably possible to mine Antarctica profitably, assuming key resource producing countries descend into utter chaos and mass violence. In the worst case scenario, it will definitely be profitable to mine Antarctica by 2100.