Every Wednesday morning, my oldest has fiddle lessons. They are at a private residence and only 30 minutes long so it doesn't leave much time to do anything except take a stroll around the neighborhood.
We walk through the quiet residential area, only a few blocks away from busy commercial streets. There is a nice playground not too far away that my youngest and I usually walk to.
This area of Edmonton hosts lively community events and cultural festivals. The Kaleido Family Arts Festival is held in September and is a great gathering of arts, music and culture. The Deep Freeze Festival in early February is a celebration of all things winter, with the addition of Aboriginal, Metis, African (and more) song and dance. Both are free community gatherings put on by Arts on the Ave, http://www.artsontheave.org, a non-profit organization whose goal is to develop the neighborhood into a community arts district.
So if you're ever in Edmonton, be sure to check out what events are happening on the Ave.