Suika is one of my favorites. It's a Japanese slice-of-life drama.
If you're interested in movies, Yasujiro Ozu made a lot of good slice-of-life movies. I think Late Spring is good place to start, but you can pick any random Ozu movie and it'll probably be good.
Hirokazu Koreeda also made some good slice-of-life movies e.g. Still Walking and Our Little Sister.
