I've been playing and enjoying the following three games. I'd like to recommend them here. I'm also looking for other similar games. So if anyone knows of any, let me know.
Each of these three games has a different setting. All are rated over 4 out of 5 at Google Play. All are one-time paid apps without any in-app nickel-and-dime scam. (I absolutely do not tolerate IAP unless it's a one-time purchase to unlock a full game.)
1. Organ Trail: Director's Cut.
It is set in a zombie apocalypse. Retro graphics, (which I really do not like even though the gameplay is good.) It is Rated 4.4 out of 5. $3 without a demo/trial version. It is also available on iOS.
2. Astro Frontier.
Sci-fi space setting. Cartoon/anime graphics. The lite version is rated at 4.3 and the full version at 4.8. The full version is $3. The lite version is free and locked out of many ships and upgrades. This is an Android exclusive, i.e., it is currently NOT available on iOS.
3. Tales of Illyria.
Medieval fantasy setting with heavy RPG components, party building and character/stats development. IMO the best of the three. It is still a trail game: players choose to which different cities/towns/villages/locations to travel as the game progresses, (i.e., it has branching trails.). This one is more expansive than the previous two. It is currently rated at 4.7 and priced normally at $8, but is currently 50%off at $4. It does not have a demo/trial version.
This one is also exclusive to Android, and I do not believe iOS would ever get a version -- because the developer has never ported his first game Legends Arcana to iOS. His new game is a huge improvement over his first game.
If anyone knows of another similar game that is rated at 4 or higher and does not have in-app nickel-and-diming, please let me know.