Since I'm likely going to be recommending a lot of these, I've decided to break the broad genres into separate posts.

First up is the Iyashikei genre!
Also known as 'Healing Effect', these shows are generally slice of life and very calming, with low or no stakes. Often overlapping with Cute Girls Doing Cute Things, but not always. K-On yes, Girls und Panzer no.

Flying Witch
The story is about Makoto, a young witch from Yokohama, who moves to Hirosaki, Aomori to live with relatives as part of her training. What follows is Makoto's daily life as she gets used to her new environment. Her relatives and the new friends she makes there are introduced to the customs and peculiarities of witchcraft.

--Not much to say about this one, except that it's probably a little bit more comedic than some of the others in this section.

Super Cub
The series is set in the Mukawa area of Hokuto in Yamanashi Prefecture, Japan. The story follows Koguma, a lone, gruff girl with no hobbies or interests. After an encounter with a Honda Super Cub 50, she begins to grow and her world expands beyond herself.

--Watching Koguma learn how much bigger the world is is *amazing*.

Diary of Our Days at the Breakwater
(Wikipedia doesn't have much about the plot, so this is all my own stuff. ALso, it's about recreational fishing, which I forgot to note before) Also known as "Afterschool Embankment Journal", it's a series about a girl who moves to the boonies from the city, who gets shanghai'd into the Embankment club by an overbearing club president and a *highly* enthusiastic childhood friend, despite wanting to be in the embroidery club (a hobby she's enjoyed for years). It ends up working out. Taught me a lot about fishing that I'll literally never use! This one can be a little bit gross at times, depending on how sensitive you are to the preparation of freshly caught seafood.

Laid-Back Camp
Rin Shima, a high school-aged girl, enjoys camping on her own. One day, she meets Nadeshiko Kagamihara, who encourages her to join their school's camping club. Together, Rin, Nadeshiko, and their classmates Chiaki Ōgaki and Aoi Inuyama travel around Japan, camping together and enjoying their daily lives.

--Peter Eng and Gryphon have both talked about this one in other threads, and it is EXTREMELY good and relaxing, and has also given me information I'll never have reason to use. :) Also, don't forget Room Camp! Which is some low-camping-activity stories set in and around the school's camping club room.

Amanchu!
Futaba Ooki, a shy girl who just moved in from the city to the oceanside town of Shizuoka, meets Hikari Kohinata, an erratic girl who loves scuba diving. Together, they join their school's Diving Club and discover the joys of underwater exploration.

--Probably not a good show to watch if you have a thing about the sea or being underwater, but if you're okay with that, it's a very introspective show, with occasional whole episodes devoted almost entirely to characters inner monologues as they go through their day, or parts of it.

Restaurant To Another World
The Western Restaurant Nekoya is a restaurant situated in a mundane corner of an undisclosed Tokyo shopping district which offers a lot of Japanese versions of Western dishes. It opens during usual business hours but is closed during holidays and weekends; with its usual clientele being the working class of the city. But secretly it is also open on Saturdays, as on this particular day it creates doorways to another world inhabited by elves, dragons, beastmen and other fantastic creatures, who enter the restaurant and partake of its exotic food, with many of them becoming regular patrons. But while Nekoya mainly offers food, it is also a place where relationships are forged, inspirations made, and salvation for the needy is provided.

--WARNING: DO NOT WATCH THIS SHOW WHILE HUNGRY. This one is based a LOT on food and how it brings people together, and holy cow, the food all looks *so good*.

Sweetness and Lightning
Kōhei Inuzuka is a teacher who has been raising his daughter, Tsumugi, by himself following the death of his wife. Having mostly bought ready-made meals for his daughter since, Kōhei's encounter with one of his students, Kotori Iida, leads him to take up cooking in order to provide proper meals for Tsumugi.

--You may have seen a video clip of a little girl who's about 40% hair by mass singing a shark song while walking down the street. That's from this show. It's an emotional show, with some fairly simple recipes you can learn to make yourself!