The following destinations are good day trips by train from Basel:
Zürich
Berne, Interlaken see below, Lucerne see below, Schaffhausen - all in Switzerland, 1-2 hours from the main station Bahnhof SBB.Freiburg
and the Black Forest - these are across the border in Germany bring a passport, roughly 1 hour from the German station Badischer Bahnhof in Kleinbasel.Colmar
in Alsace passport!, leaving from the French SNCF station, at the far end to the right of Bahnhof SBB)Lucerne
(http://www.luzern.org/). One of the most picturesque towns of Switzerland, on the shores of Lake Lucerne, with terrific panoramic views of the Alps. Flooded with tourists during the summer season, but still worth a day trip. Nice restaurants along the Reuss river, which you can cross using the famous wooden Kapellbrücke Chapel Bridge. From Lucerne, you can take an air tram up to Mount Pilatus (http://www.pilatus.com/de...) 3 hours roundtrip, including snack and enjoying more panoramic vistas, or 5 hours if you want to walk back down, recommended - but with solid shoes only. The old town also has lots of souvenir shops with T shirts and other relatively inexpensive trinkets.The Kapellbrücke is an astounding historic landmark. Built of wood, it suffered a disasterous fire in the 90s. The loss was confined to only part of the bridge and it has since been rebuilt. The history of the bridge goes back a long time and the loss in artwork was tragic. If you visit Lucerne, walk the bridge paying attention to the artwork in the rafters. This is a most delightful ten minute walk through the history of both graphic art and the skill of wooden bridge-builders.
Interlaken
(http://www.interlakentour...). Scenic valley town in the Bernese Oberland, between two lakes hence the name, and right at the center of the Alps. Interlaken is an ideal starting point for day hikes in the Alps, and for sightseeing three of their most famous peaks: Eiger, Mönch and Jungfrau. A most spectacular view is from the mountains opposite. From Interlaken train station, walk or take a bus up the road leading away from the Eiger. About 2-3 miles / 4-5 km up that road is a bus stop at a restaurant-chalet that is ideal for gazing at one of the most picturesque sights in the world! Relax, have a beer or two, order a light lunch and shoot your photos. In addition to the peaks, the view of the valley floor far below with its patchwork of farms and Interlaken itself is awesome.Lugano
(http://www.lugano-tourism.ch/). Palm trees in Switzerland? - You better believe it! At the southern end of Switzerland, near the border with Italy, lies the Ticino, the part of Switzerland where Italian and Swiss culture blend. A direct train from Basel to Lugano 3 1/2 hours crosses all of Switzerland and eventually quite literally the heart of the Alps. After the town of Erstfeld, the tracks wind their way up and then down again, using a series of underpasses and tunnels, which culminate in the 18 km 11 mile long St. Gotthard tunnel. On the way south, as the train passes the town of Wassen, you can see the same little church, perched up on a hill, no less than three times: first on the left, then on the right, and then again on the left of the train. Upon exiting the tunnel into the Ticino valley, you immediately sense the proximity of Italy, particularly in the architecture - and in the weather, which tends to be significantly warmer than in the northern parts of Switzerland. In Lugano, ride the funicular from the train station down to the lakeside to get a quick start on your excursion. There are several local cable railways and areal trams to surrounding peaks, such as Monte Bre (http://www.montebre.ch/in...), or Monte San Salvatore (http://www.montesansalvat...). Pretty little towns nearby include Morcote (http://www.promorcote.ch/...) and Melide with a miniature Switzerland exhibition (http://www.swissminiatur.ch/ie/index.asp - great for kids), both about 15 minutes from Lugano with the local FART [sic!] bus, and Como in Italy 15 minutes by train, good for shopping, bring a passport. Make an early morning departure from Basel, tour and have lunch and dinner in Lugano and return in the late evening. Wear light clothes for sub-tropical Lugano and don't be surprised by the skiers getting off the train in parkas at the mid-Alps stops.Laufenburg
(http://www.laufenburg-tou...) Not as big and well-known as the above mentioned destinations, Laufenburg is a small but pretty medieval town, half Swiss half German, divided by the Rhine. It's a pretty half-hour drive or train ride along the Rhine from Basel. You can continue the drive for up to two more hours until you get to Schaffhausen and the Rhine falls.