The objectively best recommendation here is Hexcells! Buy all three, they’re super cheap and amazingly good. It’s like minesweeper crossed with Picross, with hexes. There are bespoke puzzles in each of the games, then the last one has an infinite mode too – honestly they’re not nearly as good as the designed puzzles, not because they’re bad but because the designed ones are so, so good.
My go-to “waiting room” phone game when there’s no signal is Wordscapes. You get a selection of letters and have to make as many words as possible to fill in a crossword puzzle, so sort of like Boggle. I ignore the in-app purchases and use my brain and the coins I collect solving puzzles for occasional hints.
Vexed (also various online versions available, not sure about iOS. I was playing this on my Palm Pilot in the '90’s…) Flow Free Simon Tatham’s Portable Puzzle Collection is a zillion-in-one. not for IOS, but javascript versions are playable on that page
I was just about to suggest Simon Tatham’s collection! There’s an iOS port of them here, though I can’t vouch for how good the port is because I use an Android phone.
A few years ago, I played Hexcells until I couldn’t sleep-- always seeing those hexes behind my eyes. Wicked, wicked addicting. I hadn’t had a problem like that since Tetris.
I do highly recommend it as well, but be careful. It’s heroin in game form.
I really like mechanical puzzles where you have to move things around. In addition to Sokoban, a few that come to mind are BoxUp, Full House, Peg Solitaire, Plank Puzzle, Professor Fizzwizzle, Rush Hour, Tipover and Wriggle.
I came across this roguelike puzzle game called Mosaic featured on the Itch-io home page a while ago. I am not very good at it but I like it. It is not very forgiving…
Of the Simon Tatham collection mentioned by @zed, Net is my favorite.