Side mission ideas:

• You could help a crippled npc retrieve food
• You could have to save someone from a zombie
• You could have to reconnect the power somewhere
• You could have to deliver a package
• You could have to kill someone specific
• You could have to help someone turn back from a zombie
• You could listen to someone's life story and then help them fulfill their dying wish
• You could acquire a pet by earning its trust
• You could interact with a different community of survivors and gain their trust
• You could help in a feud between rival human surviving factions

Places:

• slums
• old corporate towers
• beach/waterfront
• amusement park
• old residential suburbs
• a school
• farmland
• forests
• brambles
• a farm maze
  
  I hope these help!