A couple that I like:

• 80 Days - it’s not free but I think it’s worth it. It’s a sort of steampunk version of Around the World in 80 days where you have to plan your routes, and buy and sell things in different cities to make money. The main gameplay is sort of choose-your-own-adventure events that happen during travel and in different cities.

• Card Thief - I just started playing this recently. It does technically have a microtransaction but it’s more like, they let you play for free if you don’t mind waiting for chests to unlock, or you can buy the game to bypass this. The main gameplay is sneaking through dungeons represented by a 3x3 grid of cards randomly drawn from the deck; collecting treasures and avoiding getting caught.

2048 but a version from F-Droid: https://f-droid.org/packages/org.secuso.privacyfriendly2048/

If you don’t mind a classic chess. Blitz/bullet/rapid/horde are different styles that don’t take as long to learn enough to have fun. Chess puzzles or against the computer are available if you want to keep it strictly single player. Lichess for multiplayer or I like chess tactics pro for puzzles.

Crosswords, there are programs like alphacross that aggregate from other sources to try different puzzles to find ones that aren’t too easy or hard.

bloons td6 is a nice cozy game, one of my faves

Tetris

You should download Mini Review

It is a currated version of the Play Store with many filters including paid/free, IAP, genres, …

The reviews are very thorough and always include a paragraph about the “presatoriness” of IAP if any

Shattered pixel dungeon has been a mainstay on my phone for what feels like a decade now

I used to play Unblock Me. Made it maybe 1000 levels in various difficulties before stopping.

Holedown

You just aim a ball and clear blobs before they reach the top. No timer. I usually play this with my screen split to YouTube.

Polytropia

Old school RuneScape, it has free “demo” version which you can easily put a 100+ hours in. And if you really love there is a subscription model that’s kinda expensive if you bill monthly, but no other micro transactions.

2048

Golf on Mars and Desert Golfing. Super simple. No ads. Its just 2D golf that keeps on going with any gimmicks.

Exiled Kingdoms, its an older isometric 2D adventure RPG. Kinda feels like it would have been made 30 years ago for pc, but it was made relatively recently for phones. I don’t think there was any micro transactions. It may have had an initial purchase price, not sure. That’s usually what I look for in a phone game. The traditional model of buying a game and then just playing a game. No gross mobile game stuff.

I liked egg inc for a while, if you’re looking for clicker type games.

Other than that I can recommend

• Stardew Valley
• Peglin
• Sudoku
• Nanograms
• Dungeon Village 1 & 2

Multiple of these are paid, but I’m 100% on board with paying a small amount for an app rather than paying a multiple of that for in-game Battlepasses and whatevers.

It annoys me a lot to say this, but Netflix has some excellent games in their roster. So if you have a Netflix subscription, check those out. I personally very much enjoyed

• Storyteller
• Into the Breach

But they also have ports of some very good PC games like Spiritfarer, Terra Nil or World of Goo.