Here - anything in the morning or early afternoon does NOT work. Why not contact area churches or other groups that have done festivals and ask what times they have done their and what the results are.
Advertising is very important if you want to reach non church members. We post our events on our church sign, take advantage of free newspaper coverage (check for community pages, bulletin board page, religious sections, etc.). Some chamber of commerce offices will list your event in their newsletter or on their sign, as will banks.
We try to get email addresses from attendees. This is no cost advertising of upcoming events.