Tinker Island is a game I recently got into. You can play it offline, but if you do then you (of course) can't watch ads for free things. It's one of those games where you mostly upgrade and wait for long periods, but it has a really addicting offline-capable mini-game that you unlock where you have to place seeds into a garden. FYI; the mini-game is proven to be impossible to complete once you hit level 165.
You can't go wrong with any game from Telltale Games, which are more interactive novels than they are actual games. What choices you make in the games have very little impact on the ending, but the stories are so well written that it's easy to forgive them. The only limitation with Telltale games' series are that if you want to download every episode of a particular series, it's usually around at least 5 gigs of storage space. So you'll likely have to delete some of your other content before you can enjoy one of their series from beginning to end.
If you don't mind spending a few bucks, there's a game called "Downwell" that's my go-to game for when I'm stuck in airports or waiting rooms. It takes very little battery power to run, and it's addicting for all the right reasons. There's no micro-purchasing, what you buy is what you get.
Another game that costs money to own is Zen Pinball. You purchase individual tables for $1-$2 each, the more expensive tables are the ones associated with franchises like Star Wars or Elder Scrolls. It takes up a decent amount of battery power, but you can get a good couple hours of play out of your system before having to give your phone a rest. The tables are very well detailed, and contain a ton of content that I have a lot of fun discovering. Unlocking wizard mode with the tables is fun as well.
Edit; also, I don't know if you heard, but Star Wars: Knights of the Old Republic and Jade Empire are both available for mobile devices. They're special editions that include the dlc, so there's things to discover even if you've played both games into the ground. There's also a few games called "Aralon Sword and Shadow" and "Ravensword: Shadowlands" that are basically cheap knock-offs of Skyrim that most people can beat in a few days, but they're still fun.