There's been a bunch of great suggestions in here.

I would like to add A-Channel https://anilist.co/anime/9776/AChannel

And Seto no Hanayome https://anilist.co/anime/2104/seto-no-hanayome

I'm guessing that you are looking for slice-of-life (SOL) anime that are also cute-girls-doing-cute-things (CGDCT) anime given that you asked specifically for something like K-On! instead of something like Barakamon or Skip and Loafer

• The Demon Girl Next Door
• Bofuri
• 'Tis Time for "Torture," Princess

Here are more CGDCT SOL anime, but these are a bit more degenerate:

• How Heavy Are the Dumbbells You Lift?
• Sakura Trick

• Aria
  • pure slice of life, heartwarming
  • start with Aria the Animation, NOT Origination despite the name
• Hidamari Sketch
  • pure slice of life, art school, comedy
• Nichijou
  • comedy, school
• Danshi Koukousei no Nichijou
  • comedy, school
• Mushishi
  • supernatural, travel
• Lucky Star
  • comedy, school
• Minami-ke
  • comedy, family

If you especially liked K-On!, then I guess Lucky Star is the closest one, with no music band stuff. Note that LS has tons of references to other media, so if you're new to anime, 80% of the jokes will fly over your head.

Nichijou is very comedic, and so is the other one with Nichijou in the name (they are unrelated, just the generic term "nichijou" means "daily life").

The Aria series is my favorite; it's very slow, to the point of being boring, but you grow to really love the characters and end up bawling your eyes out when it ends.

Haven't seen K-On myself, a couple of slice-of-life anime that pops up in my head.

• A Place Further Than the Universe
• Skip and Loafer
• Miss Kobayashi's Dragon Maid

I think "Is the order a rabbt" and "Lucky star" are most similar to "K-ON!" but without music bands. If you ok with camping then "Yuru Camp".

If you want something that's airing right now "mono" fits a bill. It's about a girls taking pictures with various cameras.

There are a lot of them, don't know what you will like so I will a few of my favorites

1. Horimiya
2. Daily lives of Highschool boys (more comedy than SoL)
3. Aharen san wa Hakarenai
4. Akebi Chan no Sailor Fuku

Azumanga Daioh, still the GOAT.

Yuyushiki, maybe? It's slice-of-life with three girls in a computer club instead of a music club. I liked K-On's humor more, but I remember thinking they were similar when I watched it a long time ago.

Skip and Loafer, that seems pretty similar to K-ON

Hidamari Sketch

Yuru Camp

Asobi Asobase

Asteroid in Love

Yuru Yuri

Yuyushiki

Love Live! School Idol Project

Non Non Biyori

Azumanga Daioh

Akebi's Sailor Uniform

Diary of our Days at the Breakwater

I don't know if I'd call it slice of life, but you might like Anne Shirley (currently airing). For non-airing stuff consider Mr. Villain's day off, Interviews with Monster Girls, Gabriel Dropout and My Dear Friend Nokotan, in that order.

Shikanoko Nokonoko Koshitantan

Nichijou

Yuru camp