This app was mentioned in 8 comments, with an average of 3.50 upvotes
Exiles: https://play.google.com/store/apps/details?id=com.crescentmoongames.exiles
Its been a while; but its basically Ravensword: Shadowlands in SPACE!! Though admittedly its more like Fallout meets Mass Effect (On paper, don't push your luck). Its basically an open world action RPG that takes place in a Desert Wasteland. There's really not much to immerse yourself in, but if the running, riding, shooting is what you think makes a good open world sandbox RPG......you'll also need to know that its buggy .
Oh and there's a pretty solid character customization too as with all open world RPGs made by Crescent Moon Games.
Gangstar Vegas: https://play.google.com/store/apps/details?id=com.gameloft.android.ANMP.GloftGGHM
Imagine Saints Row: The Third with free DLC but microtransactions that try its best to ruin your experience. The game is pretty fun though its far from being as "wacky" as SRTT since the progression is more down to earth. You'd have to enjoy grinding if you want to get the most out of this game. Don't be fooled by the Play Store's screenshots, I think you'd have to integrate this game into your way of life to get that far.
The open world is pretty huge, the graphics are really great (it runs smoothly on my 1.2 ghz Quad Core) even at the lowest setttings which makes driving around it pretty fun and relaxing (You can even make money out of it by exploiting Chop Shops; more on that later). It all feels like a living breathing environment (of course, don't expect any deeper immersion than kill, gamble, and drive).
The ingame economy is a joke (Which is sad since this game could be so much better if it was "balanced"). I wouldn't go into deep Confucius-level detail, but IIRC a Medikit costs 5000 dollars...do the math!! Chop Shops like I said before are pretty much (potentially) the BIGGEST non-gamble involved income you'll ever have in this game. You basically steal a vehicle, send it to a garage door, and profit!! Looking at deployment prices helps; especially since you get more or less the same amount of cash...do not bother looking for ones that cost gold to purchase, they give you piddly squat.
You don't need an Internet Connection to play it, but you can get daily rewards if you turn it on...though don't expect it to always work. Also this crashes a lot before I even get to the menu (though after going past the menu, its all good), I played it on a 1.2 ghz Quad Core with 1 GB of RAM.
There's also Exiles free in the next 5 hours https://play.google.com/store/apps/details?id=com.crescentmoongames.exiles
EXILES - hasn't been updated since 2015, might not even work at all but it's basically Sci-fi Aralon
Not RPGs but excellent Open World games: Brightridge, Vandgels and Wilderless
Exiles is a sci fi rpg, here's link : https://play.google.com/store/apps/details?id=com.crescentmoongames.exiles
Exiles is a sci fi rpg, here's link : https://play.google.com/store/apps/details?id=com.crescentmoongames.exiles
Fairly decent character customization and open world. Another good one is KoToR (as linked by Punkandy26).