I live in Scotland (Glasgow). THe place was £170k to buy and needed about £40k ish work done to it.

The £40k came out of savings, £70k deposit and you end with a really cheap fixed mortgage on £100k that comes to £445 a month, in fact it's low enough that I overpay it some months by double to get the mortgage paid off quicker.

Glasgow is tiny compared to NYC, SF, LON, etc. In an equivalent sized city in the U.S. you could easily find a house for $200k.

it's probably not size but rather the "hotness" of the city, i.e. afaik Rome is the biggest city in Italy by far (maybe the biggest in EU as far as actual size is concerned) but cost of living is quite low compared to other EU capitals and even other cities in IT, Milan i.e.