Horror Manga

Some suggestions off the topic of my head:

Another

Sugiru Juunana no Haru is adapted from a horror-mystery novel written by the wife of the writer of the novel from which Another was adapted. It is not gory at all like Another, and the themes are nothing new in horror, but I was still a fun, short read. (If you read light novels, Shizume no Itaka is of a similar nature as well.)

Shi ni Aruki is similar to Another in concept, but much more of a slowburn and with no gore, only minimal blood.

Higurashi

Umineko no Naku Koro ni is the natural suggestion. The horror element is much weaker than in Higurashi and is mostly overshadowed by the fantasy, mystery and drama, but I think some episodes, especially Ep 2, are still very strong in horror. (Umineko is still usually classified primarily as horror, I think because of association with Higurashi.)

Happy End. is very similar to Higurashi at first, and its influences really show; however, it becomes quite different towards the end.

Higurashi was originally a visual novel before it was adapted as a manga. Its influence is even greater in VNs than in manga, I think, so you may want to expand to this genre for more horror-mystery with a psychological bent

Corpse Party

Dolls Fall is from the same author. Not the best plot in the world, but the gore is very colourful - you can tell the artist had fun drawing it.