Put them high in corners where walls meet the ceiling. This gives a wide view of the whole room, not just the doorway. I always use pet-immune models now to avoid false triggers from animals. It really improves coverage and keeps the system reliable.
Didn't @abby675 have a point about pet-immune models? I saw a tech blog that said even the best placement can't fix a bad sensor... so maybe starting with the right gear is just as key as where you point it.