Tokaido, the very popular board game about traveling across Japan, is coming to mobile very soon, and from what I've seen so far, it looks really nice. The game will be available for both smartphones and tablets and on both iOS and Android. The app will let you play solo against the AI but also in local and online multiplayer. As you can see from the screenshots below, the art looks lovely and the port retains the physical game's overall style.
If you haven't played Tokaido before, you and other players travel along the East Sea Road connecting Kyoto to Edo, stopping at the various stations along the road from which you can buy all kinds of souvenirs, meet interesting people, taste the cuisine, and much more. The order of play is from the farthest to the closest, which makes this game less about rushing to the end and more about being clever about when and how you move. Tokaido should be coming out soon, so keep an eye out if you've been looking for a good board game.