Three countries in an hour? Why not? This is, after all, a three-country corner with France, Germany, and Switzerland coming to a point around the Rhine River. Basel is the ideal anchor city to see all of these countries and some of the most noteworthy sights in them. First stop: The Alsace region of eastern France. This region toggled between the hands of Germany and France for well over a hundred years and is rich in history, natural beauty, and wonderful wines.
Strassburg is about a two hour train ride from Basel. The historical significance of this city can be seen everywhere. The gorgeous Notre Dame de Oeuvre towers over the city. A not-so-quick climb to the top is definitely worth the view.
Colmar, an hour closer to Basel than Strassburg, is ideal for those looking for the Alsace-style excursion without traveling two hours to do so. Noteworthy sites include the Musee d'Unterlinden, home to the Issenheim altarpiece amongst other works, the Saint Martin cathedral, and the Musee Bartholdi, the sculptor of the Statue of Liberty.
Next stop: The Black Forest. A trip to Freiburg, renowned for its university and position within the Black Forest region, is a short 40 minutes away by train. Rebuilt after being destroyed during World War II, the city can appear to be older than it really is. A side trip to the Black Forest is just a skip away.
In Switzerland: Augusta Raurica is an excavated Roman city a few minutes outside of Basel. Many of the sites can be seen free of charge, but the museum costs about $3.