The Downtown Phoenix Public Market is an excellent community gathering place. The organizers are really supportive of community groups (my students had a table there to conduct a class project with no hassle or cost and a great location).
There are lot of great vendors. Although some of my favs are hit or miss- Strawberry, AZ goat farmers, where did you go??? And the caramel popcorn guy is no longer there :( This is not a huge market a la Madison, WI, but it is year round and provides an opportunity to feel like you are making a difference in the emerging downtown community.
Some weekends there is a nice mix of jewelry and art. Wednesdays are great for veggies and chatting up vendors. Definitely go and bring the visitors to a no cost event. Get some hot cocoa from Wei in the winter and enjoy your neighbors.