It can be very expensive to insure in Basel, but will go down once you have some car insurance "history" here is Switzerland.
When I first got my car here in Basel I paid Sfr 2500 a year, but now pay "only" Sfr1100. The insurance company made it very clear why it was expensive:
1) Location - I lived on "Basel's Worst" street for claims at the time (It is also one of the longest - hence more claims!).
2) I was an auslander living on above street
3) The car was too sporty...

4) The car was brand new.
5) My auslander permit was only a B.
The yearly costs dropped slowly every year except the years when I received my C permit and when I moved out of Kleinbasel, both dramatically reduced the yearly amount.
Pat