Horror anime for someone new?

I have a lot of downtime for the next week or two and I've been considering giving anime another shot - tried before but couldn't really get into it.

I'm a huge fan of horror. Are there any good horror anime that a "beginner" would like?

It can be niche, all I care is that it's: (1) considered great by a decent amount of people (2) something that'd appeal to horror fans.