Matt, if you are into running, then join the Basel Dragons running club. They meet Monday and Thursday evenings at 1830, at their clubrooms which are literally under the Weststeinbrucke ( the bridge near the Kunstmuseum) They run in 3-4 groups of varing speed and distance and have regular social events too. Do a google for the webpage, or look for them via the Basel groups on the www. meetup.com site. Members are from various countries and of varied ages.
I second the idea of you joining the Basel Couchsurfing group www.couchsurfing.org
- go to one of the Monday evening meetings to see if you enjoy them . they tend to get active with bbq's etc over summer.
Are you coming here to work? Or to study? Either of those are likely give you the opportunity to meet people you can also socialise with. :-)