Hi Tere!
For a start, I would recommand the "Parc linéaire des rivières Saint-Charles et Duberger" trail, it is a 32 km long very nice trail that runs from Lac St-Charles (northern suburb) to the Quebc'S harbour. Of course you can easily park near the trail in many places and do only small portions of it, especialy in the southmost part of it. Chek that bookmark : Parc Linéaire des rivières Saint-Charles et Duberger".
On the historic side, there are many caches located in the old city; among those I suggest you check the ones placed by SPUQ (1 easy 1 setp multi, 3 micros and 2 smalls) that are intended to show you different faces of the old city. Also, don't miss GC15RDD, a cooking receipes sharing oriented cache - I still wonder how a cache that big had survived until now in the middle of the city.
Of course there are many many more great cache to discover int the city.
Have a nice mega-event!