High speed being? Unless you need gigabit speeds any of the provincial capitals will have at least 100Mb service. Some areas up to 200Mb. Even smaller towns will.

Note I said some areas. The city centres are most likely to have the fastest speed. You are not looking for rural so most areas will be served by at least 100Mb.

If you need 1GB woe is you. There are a few neighborhoods around the country but that's about it. I think mostly in Milan.



Which gets to the problem. Just because the neighbourhood offers 100Mb doesn't mean the rental will. You'll need to ask the landlord.

October is already off season outside of the big three. Definitely the coastal towns will have gone at least partially dormant.

You could do worse than picking a place slightly outside the centre of Rome. Not the outer suburbs . Just past the Vatican maybe? Or in the other direction just outside the Colosseum area?

Your main problem is 1 month is a tourist rental. Your paying tourist rates not long term rental rates.