I like to fool around with games on Facebook—they tend to be nice little timewasters. But if you've played any of them at all, you know their pitfalls—invite (pester) friends to get ahead, post innumerable things to your wall, buy stuff with RL money to advance, limited amounts of energy to play, etc.
However, I'd like to direct your attention to a wonderful gem of a game—The Grinns Tale. It has a fantastic soundtrack, the artwork is beautiful and original, the sprites are absolutely adorable (I love how they "talk"—I will click on things just to hear them vocalize), and it has a great sense of humour. And the best part is, you don't have to deal with any of the things I mentioned in the first paragraph. Yes, there is a cash shop, but you don't need it at all if you don't want it. You can adventure and quest to your heart's content. The only thing that limits you is your resources to buy food, which your characters need for stamina—but you can build buildings to make that. It's part of the gameplay. And yes, you can add friends and visit them, but they're not needed in order to play or advance.
It's not grindy at all; I love playing this thing. If anybody wants to add me, feel free; my Facebook page is here.