Nikoli Puzzles
nikoli.co.jp
nikoli.co.jp
And for fans of Konami games, this app is fun too: https://www.konami.com/games/us/en/products/pixelpuzzle/
And apparently there's an app for iOS too.
It's mostly in German, but each game page usually has a rules section in English and links to other sites with the same puzzle type.
Light up/Akari I have never quite gotten. It's either too simple or too hard, after learning the common patterns. I often end up just trying to fill in something, and backtrack when it doesn't work. Not as satisfying as deducing it would have been.
Hitori is nice, albeit a bit easy after having found the patterns. But relaxing to just comb through a few puzzles.
Shikaku, I prefer Tentai Show which is similar but arbitrary rotatable shapes instead, a bit nicer patterns to learn.
To an outsider, it looks a bit like minesweeper.
That being said, KenKen does seem to fall into a similar class of constraint-based, language-agnostic games.
[1] https://en.wikipedia.org/wiki/Nikoli_(publisher) [2] https://en.wikipedia.org/wiki/KenKen