-Time based (Day/Night cycle with tasks to complete)
-Open world (A world map and explorable world in which to complete tasks)
-Different activities available at different times of day (possibly even times of year?)
-Rep (Building up reputation in the "town" or "world")
-Choosing to adhere or not adhere to the rules of the "town" or "world"
In terms of games that already exist I was thinking of 'Final Fantasy Crystal Chronicles: My Life as King' a game in which you play a young king who has to help his kingdom grow. Each "level" is a day cycle. You assign people in your kingdom to do different tasks that day and help build new buildings. When the day cycle is up you see how far you have progressed while he is 'asleep'
|Gameplay from Final Fantasy Crystal Chronicles: My Life as King (2008)|
I was also thinking of Animal Crossing. A relaxing game set in real time in a sleepy town by the name of your choosing, in which you can choose how to while away the day doing activities such as fishing, visiting neighbours, and collecting fossils for the local museum.
|Gameplay from Animal Crossing: City Folk (2008)|