You NEED to go to places that interest you, not us. For example, Stonehenge doesn’t interest me, so I wouldn’t go there and ditto Highclere Castle (where Downton Abbey was filmed), but I love National Trust properties Sissinghurst gardens in Kent and Cragside in Northumberland.
You brief doesn’t cut out any of Europe. If budget is a consideration, London, Paris, Venice, Madrid, Switzerland and Scandinavia are more expensive.
Do you want one home base or two? If one and you want to explore other parts of Europe, then you need to be based near an airport where the value airlines are based e.g. near Gatwick or Stansted not Heathrow in London. Alternatively, would you prefer to cover a smaller area, but see it in more detail? A month whilst working isn’t very long to explore a whole continent.
Most places have a decent WiFi connection although mobile phone signals can be spotty in rural locations.
Exactly when would you be travelling? If later in the year and you want warmer weather, then Portugal or Spain would be the best option.
Do you speak any languages other than English?
For different reasons my suggestions would be:
London - good access elsewhere, fantastic museums, transport, markets and history.
Edinburgh, Scotland - fantastic scenery on the doorstep plus history. Better for whisky than wine.
La Rochelle, France - great food, markets, history and a lovely coast with wine regions nearby, but less accessible to other countries as the airport is small.
Lisbon, Portugal - better weather and ticks your other boxes.
Tavira in Portugal smaller town with good access to Faro airport.
Seville, Spain - as Lisbon. I don’t like Spanish dining hours- I never get used to eating dinner at the time I am usually going to bed!
Budapest, Hungary - a great vibe and feels very different to say London.
Berlin - modern history, great airport for connectivity elsewhere, markets etc.
You could take a map of Europe and both stick a pin in blindfold and see if either options would suit and take you somewhere unusual.