Monaco

Monaco is small enough to walk across in 45 minutes. The Casino de Monte-Carlo is the postcard but most of the city is the rest — the old town up on the Rocher with the Prince's Palace and the cathedral where Grace Kelly is buried, the exotic gardens cascading down a cliff, the Oceanographic Museum (built into the cliff edge, founded by Albert I — the aquarium is excellent). The Grand Prix circuit is the city streets, with the grids still painted on the asphalt year-round. Bring a passport for the photo at the border.