Beastie Bay
This is another one of those Kairosoft games, but I found it to have much more depth than their typical fare (plus it's free with a banner ad, removal costs a few bucks).
It has a "gotta catch 'em all" beast battling system on top of the classic Kairosoft style sim stuff. There are a good amount of secrets too. Definitely worth playing.
Also they have a pay4currency system, but the coins are also received randomly from doing dungeons, and rarely if one of your beasts harvests a 5 star land square. Later in the game you can set up beast houses surrounded by 5-star environments, which can allegedly net 100+ coins an hour (45 beasts equipped with +work bandanas surrounded by eight 5-star squares. It is NOT pay to win, the coins are needed to do some content, but by the time you really need them, you can farm them.