If you're looking for anime similar to Natsume Yuujinchou (Light Novel), you might like these titles.
The series centers around two cats: a younger sister named Neko, and an older brother named Mata. Neko is a nekomata (a mythical two-tailed cat), innocently selfish, and spoiled by her brother. Mata is a neighborhood cat with an eartipped mark as a sign of being neutered. They meet under a streetlight in the city at night to talk.
30 year-old web designer Souta Tawara takes a leave of absence from his job in Tokyo to return to his hometown and sort out his family's affairs. His recently-deceased father's udon restaurant is now closed, and the house Souta and his sister grew up in stands empty. Ridden with guilt over disappointing his father, Souta is beginning to doubt the choices he's made in life thus far. While trying to figure out how he should move forward, he meets what appears to be a small boy sleeping in one of his father's old kitchen pots, but who turns out to be a shape-shifting tanuki! Cute, playful and full of energy, Souta names him Poco and the two develop a strong bond. But now he faces a conundrum: should he quit his job in Tokyo and remain in the countryside, or will he again leave his childhood home in favor of the big city, leaving Poco all alone?
Shizuru and Mizuki are two quiet sisters who have a foot in the world of the supernatural. While Shizuru can see the spirits and monsters who haunt mankind, Mizuki can't help but become possessed by them. Together, the duo live with their grandparents and are taught about the spiritual world from their grandfather, a powerful exorcist. In the serene countryside, the girls will learn about the ghosts and goblins that co-exist in our world, while also learning about themselves and their abilities.