There may be others but those are the ones I know of.
Julie pointed out a great dog park that is off leash right along the Deschutes River and The Old Mill. Superb location for the for both you and your best friend. The trail system also runs along the river so once finished with the off leash portion - you can always take a hike up the river towards Bill Healy Bridge or you can also meander along the shops and Ampitheatre at The Old Mill. The Ampitheatre is a great place for frisbee or playing ball if there is no music venue that afternoon or evening. There are also trail systems that open up after September where you can run your dog off leash. I especially like Benham and Dillon Falls just above The Seventh Mountain Resort. You will need a forest parking pass but these are available in The Old Mill at REI. Hope this helps a bit. The other two sites I would visit for more info on Bend and local amenities are: http://visitcentraloregon.com/ and http://www.visitbend.com/ .
Hope this helps in your visit.