I lived near Basel for about a year starting in 2001 and loved it! Nearly every weekend a new event takes place in this bustling yet maneuverable city. There are over 20 museums in the area and most, if not all, are accessible by public transportation. There are so many excursions from the three-country corner that it is simply amazing the number of things that could be seen on just one visit. Strasburg, France; Freiburg, Germany; the Black Forest and the ancient city of Augusta Raurica are just a few of the possible day trips one can take from Basel. Basel may seem off the beaten track for those who want to see the "typical" Swiss scenery, but for those who want an intersting trip no matter what the weather, I would suggest Basel, Switzerland.
Quick Tips:
Bring your camera!
A word to the wise: Swiss German is a very strong German dialect. You may not be able to understand the local dialects, and if you know High German, you may get nervous. Don't freak out! If someone starts speaking Swiss German to you, just ask them politely if they could speak in High German. English is widely spoken, but knowing a few German words would certainly be helpful.
Another important point: Swiss Franks are the common currency; Switzerland is not part of the European Union so don't expect to be able to use your Euros. There are ATMs around the city, including in the main train station. Exchanging money is a rip off unless you exchange a lot, so the best bet is plastic.
Best Way To Get Around:
FYI: If you arrive at the international airport that France, Germany, and Switzerland share, you can take a bus to the Basel Train Station.