Lots of things to do for several days. I drive up in a 4-5 day road trip, so I need some down time in town before I fly out into the Barrens. I typically spend 3 days in town before flying out, and a day or two when I fly back in from the bush.
All good advice listed in the above posts for the places to visit.
Weaver & Devore is a major must-do. Winter clothing upstairs is on the floor all year round.
The Yellowknife Book Cellar bookstore is fantastic. I spent alot of time in there.
For a high quality selection of unique northern designs on T-shirts, aprons, and bags, drop into INKIT, at the corner of 48th and 52nd. They also have cool free notepaper pads with caribou along the top.
http://www.inkit.ca/tee-room/I go grocery shopping (for my B&B food plus road food), at the CO-OP which is a huge very nice grocery store. You can also buy your NWT fishing license there.
Walking or cycling in Old Town and checking out all the float plane bases is fun. Climb up the stairs to the Pilot's Monument.
Years ago I bought a collection of the pilot topo maps for the entire mainland arctic and sub-arctic, which have very detailed map information. These are a nice scale to do large scale route research on. I forget which shop I bought them in, but ask around and you may find it. The maps are a good investment.