If you are into running at all, join the Basel Dragons Running club - it caters for all levels, from purely social joggers to serious athlltes, but also has a good number of social events ( there is a bar at the clubrooms.) It's an international, English speaking group. They meet 2-3 times a week. www.baselrunning.ch
Or the very social Basel Hash House Harirers (the drinking club with a running problem.) http://basel.harrier.eu.org/
Trekking - good way to see Switzerland: sign up to the Zurich trekking group through the www.meetup.com
site. All ages and nationalities, with various walks happening every weekend anywhere in Switzerland.
Book clubs: watch the events calender on this site.
Check the Meetup site for other interests, including the BASS page, which is a Basel based group that has a variety of things to do.