It really comes down to your wallet.

There's plenty of 150/200/250 m^2 flats in Italy (Rome and Milan especially), but they are very expensive.

Here's a non comprehensive list of actual apartments above 250m (I didn't filter by flat, but you can see plenty are) and this is only the core center of Rome (what would you call downtown), not the entire city.

https://www.immobiliare.it/vendita-case/roma/?criterio=rilev...