Pullman is a pretty safe town. In almost 10 years there I only ever felt unsafe when The Big Thing happened in 2022 and that was a crazy fluke situation. There are many apartment options- by #, probably most of the total WSU student population lives in "apartment land" which is the area north of campus (Aspen Village, Pine Ridge, Maple Valley, Cougar Ridge, The Grove, Pimlico, Birch Hills, The Retreat, The Flats, The Annex, etc). These are walking distance to campus (20-30 mins to the VTH probably) and on the bus routes. There's kind of something for everyone in this area.
Just north of town there are newer complexes (The Hills, Aspen Heights) - further from campus and not on official bus routes but I believe they offer their own shuttle to and from campus/grocery stores? These are more expensive and have lots of amenities.
Many vet students rent or own manufactured homes and there are a few communities in town - Campus Vista and Golden Hills are the "nicer" ones as far as I'm aware. I heard less than nice things about Terrace Estates from classmates.
There are more options off of campus - Military Hill (region NW of campus/W of Grand Ave), Sunnyside Hill (region SW of campus/W of Grand Ave), Pioneer Hill (region SW of campus/E of Grand Ave), and College Hill (region N of campus) have some properties for rent from private landlords and smaller rental companies. Your mileage may vary w/ these companies. The age-old rule in Pullman is do not rent from DRA. I had a good enough experience renting from DABCO for cumulatively 5 years. Nobody loves them but I'd rent from them again if I needed to.
Hope that helps a little!