Luxembourg City, verdict by verdict

Luxembourg City may be Europe's most underrated capital: a fortress town built on a gorge, where the old quarters of the Ville Haute sit on a sandstone promontory above the Alzette and Petrusse valleys and the Casemates tunnels underneath are a UNESCO site in their own right. The views over the Grund from the Chemin de la Corniche do the selling, and the whole place runs at a calm that bigger capitals forgot.

The straightforward frame is scale and sedateness: this is a compact, quiet, well-off city rather than a blockbuster, and the evenings stay gentle. Restaurants and hotels run Swiss-adjacent on price, the terrain means steep valleys and plenty of stairs, and two days covers the casemates, the Grund, the palace front and the museums. The rest of a trip belongs to the country's day trips, since Vianden's castle and the Mullerthal rock trails are excellent and under an hour away.

The unique practical quirk is that all public transport nationwide is free, trams, buses and trains included, which turns the whole country into an easy day-trip network. Two days for the city itself, a day each for Vianden and the Mullerthal, half a day for the Moselle valley if wine interests you: it suits travelers pairing capitals, slotted naturally beside a Brussels or Trier itinerary rather than carrying a week on its own.