If it's free to play, it's probably crap.
You're only going to get a good experience if you pony up money and pay. Usually that means buying a mobile port, like KotoR or Final Fantasy. But at that point, you mind as well just play those games properly on console/PC with a big screen, not on your tiny little screen covered by your thumbs.
The one, really good mobile game
that works best as a mobile game that you pay money for and you're done, is
Jet Cars Stunts. It's a simple, skill based game where you fly a car with a rocket engine through increasingly harder and harder levels. You fly off ramps and need to use the fuel to reach the next part of the course, but you have limited jet fuel so you have to conserve your rocket bursts. The game also uses the phone's motion system to steer, so there's skill involved in angling your rocket thrust while you are flying. It's simple but a ton of fun. Whenever I'm out and have time to kill, I'd whip out my phone and play this.
Otherwise, if you REALLY want a "free to play" mobage, then I'd probably recommend
Granblue Fantasy. The devs are very generous and I have 120+ characters just from logging in during events for free, no grinding or laying down money required. It has an official English translation built into the game and has a sizeable community in the West. They don't wave the cash shop around in your face and there is no grinding required to get through the main story (which is the main appeal of the game) and there are no difficulty walls forcing you to spend.
You just need to be using either Google Chrome or the Safari browser.
- Go to グランブルーファンタジー
- Click the "Set Language" drop down and select English
- Click "New Game
- Play through the tutorial
- Create a Mobage account. Chrome automatically translates the page for you so it should be easy, standard account creation process. Sign in Granblue with the account and you're in.
Now is a great time to get in. Every day for the next week, you can log in and get 10 free draws. After next week, they start the gachapin event, where every day you log in and you will spin a wheel and randomly get anywhere between 10 to 300 draws, going through the first few weeks of January. You'll get dozens and dozens of characters for free for just logging in for 30 seconds every day, barely any effort required.
Save your crystals.