If our corporeal undead needs to consume something to remain animated, is it really dead? Logically the answer would be no, but we accept the idea that vampires need to consume blood, as if a dead body has any ability to process liquids, not to mention oxygen in blood. What else might our undead need to consume? Souls is a good answer, as is energy of some kind. Maybe there’s a supernatural substance they need. In SF, this could exist only in space, causing the undead to be a traveler.
If we’ve invented plants or animals with special properties, perhaps our undead is compelled to feed upon them for some advantage thus gained. Decide if our undead can’t survive without it or just gains something else like abilities. Or maybe it uses narcotics to dull the misery it feels. Imagine a drunk undead. Finding that narcotic would give it a goal.
Our undead might be consuming out of habit, as in the case of a primitive, mindless undead. In this case, it may not even be aware that it can’t digest food, or that drink just leaks out of its innards. This can give our undead a typical, identifiable appearance—freshly stained with food and drink.
Spiritual undead have no body to consume with, but physical items aren’t the only sustenance available. Maybe the spirit wants or needs to feed on emotional turmoil it causes. Or it could drain the life energy from the living. Or devour their soul. It can feed on magic or energy from technology. Are there supernatural phenomenon that attract spirits? Can our species harness those and use them as a lure?
Corporeal undead have to be somewhere when not terrorizing people, so decide where it resides. We’re looking for a dwelling type more than a specific place, unless we’re creating something that’s only found in one region of the world. Do they return to a grave or spend time in caves or abandoned ruins? The latter is arguably the most interesting. Undead are sometimes depicted as being only a creature of the night, but they still exist during the day. There’s no particular reason they must be in hiding, with one obvious exception—if they’re hoping to do bad things without getting caught, fewer people are out at night and they could meet the goal more easily.
Spiritual undead have less need of a residence but are often thought to be tied to a place by sentiment. This is usually a home or the place of a big event, including their death. If they died long ago, other things could’ve been built there since. In space faring stories, an individual spirit could end up on a ship that takes it away from home but the desire to return home is a character issue, not an undead type.
Aside from the mortal world, is there somewhere they go when not haunting someplace? This is something few creators address. Are they in an afterlife? Do they have any sense of time passing? Are they just dormant like a hibernating bear? While this doesn’t need addressing, it could help us imagine something unique.