Hello Yanni, welcome (back) to Basel and to the English Forum as well!
If you check down at the Events section of the forum, fairly often there are things us Baslers are getting up to... the soonest I can think of off the top of my head is the Basel Expat Expo which takes place this Sunday. As it is a commercial event, I think it is listed appropriately in Commercial Events.
Meanwhile, depending upon what you're into, there are lots of things to do! There are all sorts of clubs (running club and book club, just to name two), or more social Curry Nights that take place on a monthly basis and other things like that.
The end of the month a few of us are thinking to head over toward Weil am Rhein as there is a Medieval Faire going on that weekend.
Hopefully see you around sometime!