Datasport.ch lists a few events during the time you'll be here.

Feeling up for the Zurich Ironman July 13th?
No? The regular triathlon is the day before, or you can race up a mountain instead. (Although the Zugspitz one is in the German Alps, which is a bit far from Zurich.) If you're looking for something a bit less extreme, there's also a 14.5km running race happening not too far from Zurich on the 18th.

Have fun!

Heather