The iOS app is my favorite timekiller. It doesn't hide the clock, it starts up really fast (no splash screen), it has no ads, it uses only 3.7MB storage, and it's free.
Slitherlink is incredible, you learn to recognize more and more patterns. And when you have mastered one variant, you can try with honeycomb pattern instead of squares or other shapes to explore new patterns.
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.
Most of these games are constraint-games, including minesweeper. So I wouldn't be surprised if they can be reduced to each other, or at least sort-of.
When playing the puzzle collection by Tatham linked here, I often find that new patterns I find in one type of puzzle can be reused in others.
There’s a nice online collection of these style puzzles at https://www.brainbashers.com/today.asp. I usually do the hardest Slitherlink, Hitori, and Ranges problems daily, for years now.
I have a book of these on my desk right now. If you are not in Japan, I highly recommend ordering directly from the publisher. The books usually have English rules, but if not they are available on the website. It is really nice taking a break from screens and chipping away at a few puzzles.
If I've researched this correctly, I believe that "Nikoli puzzles" are not a formal class of puzzles; rather the terms refers specifically to the publisher of these puzzles [1]. KenKen, on the other hand, was invented and trademarked separately by Tetsuya Miyamoto [2].
That being said, KenKen does seem to fall into a similar class of constraint-based, language-agnostic games.
Ken Ken differs from most of them in that it actually has math, whereas in the other games the numbers are really just symbols that could be anything (sudoku) or just counts (loopy/slitherlink, I think).
