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

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

Azumanga Daioh, still the GOAT.

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

• 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

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

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”.

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.

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.

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

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

Shikanoko Nokonoko Koshitantan

Nichijou

Yuru camp