It’s usually based around the monster, they’re either grazing grass most of the time (Weresheep, Holstaur), trying to find a host (Parasite-type monsters), trading with monsters/humans (Dwarves, Danuki), or finding a master (Kikimora, Shoggoth).
I believe predator mamono just hunt for husbands and food and maybe have some available hobby or place of interest within their territory.
WG1 explains that wild mamono don' care much for their living space until they get a husband. Though not muhc o what they actuall do with their time until then.