Yellowknife is small, as in you can walk the whole town in half a day. But give yourself the full day to take in the hike around the lake, a chance to pick out some white fish from the Great Slave Lake at the fish truck, which is parked in front of the KFC and visit the local art galleries and gift shops.
In terms of where to dine, I'd recommend Le Frolic for more upscale and the Knight Pub for casual dining. There really are not more choices. If the Wild Cat cafe is open, check it out, as it's historic, and the Bullock Bistro in the old town is full of character.
Obviously don't forget to take in the floating boat homes. One of them is even a bed and breakfast, which you can book through airbnb.com.