The Sims (Free Play)
We can't forget The Sims. This is one of those games a lot of people played in their childhood. And if you're a Millenial, now is your chance to enjoy what we all dealt with.
The Sims Free Play is exactly as it sounds. A completely free (offline) game that lets you create a family or an entire neighborhood. It's the original "simulator" game. With this release, you do have in-app purchases you can make, but it doesn't actually cost money to play. Although we're pretty sure you'll end up spending money somewhere.
So, build a house, fill it with people (sims) and enjoy all this game has to offer even without the internet. Some purchases won't work until you get online.