I would market to all of the surrounding cities - even if they are 20 min. to an hour away, as well as all local businesses there. For every person that can't afford to move right now, there are several that desperately need to move to lower their expenses and may not know what their options are.
Another great place to market to is the local unemployment offices. Many apartments I've worked with have had great success with this as so many people who didn't "previously" qualify for affordable housing now qualify.
I would also market to the other affordable housing properties, housing offices, etc. in your area and in surrounding cities. Many times someone may not be able to find an opening in the City they're in, but could transfer to another City where the housing program has spaces available. Or, your competitor could be turning people away because they don't have the floorplan/type available that a customer needs, not knowing that you do have it available.
Kudos on giving great service and activities for your residents