Vienna

Vienna's City Airport Train makes the trip non-stop to Wien Mitte in 21 minutes, and from there the cathedral and the old center are a short metro hop or a walk away. The cheaper S-Bahn covers the same line more slowly if time allows. The Ringstrasse wraps the best of the city into one loop: St. Stephen's Cathedral, the Hofburg palace, the State Opera and the museums all sit inside or along it. Stop for coffee and cake in one of the grand cafés, which suits a traveler running on airline sleep. Five or six hours on the ground gives a comfortable visit.