I just remembered that GTA - San Andreas had that stupid dancing minigame, as well as various arcade machines you could play.

Saints Row 3, I really prefer the slapstick humour compared to the GTA series.

Yes, indeed. Although the controls were quite similar to the usual ones. And there were the other diversions: rampages, and playing police, paramedic or fire fighter...

Vice City also had that, as well as a remote plane one, not counting the plane bomb mission of course.

Now that I think about it, there were remote control games all over that damn town.

Might and Magic VI. However, don't expect cheesy gameplay with hand-holding/game-breaking features like level-scaling and such. If you will go to Dragonsand at start of the game, you WILL die (most likely even before reaching it if you don't use hidden shortcut).

The Witcher series.

Well TW1 has a little open world feeling in the middle, once all of Vizima and the swamp are accessible. Still, you can't go back to Kaer Morhen or the outskirts. And once that (big) part is finished, you are always tied to a rather confined area.

TW2 has no open world feeling at all. The areas are certainly no "story tunnels" a la COD, but they are rather confined.

TW3 is of course open world, as I wrote above, and for me the first game that manages to combine a compelling story with free-roaming since Morrowind. But it has not the kind of diversions other games have (like growing you own garden and cooking meals or the GTA shenanigans that got more and more with each installment. There's Gwent of course, which is considerably more complex and time intensive than the old dice poker (which I miss a little). And there's horse races and boxing. Still, in games like Skyrim you can ignore all quests and callings and live a life as a lowly farmer (some people did so). Not possible with The Witcher. Of course it would not really fit either. The Witcher has always been about stories, and stories need to move forward. On the other hand with all the freedom the likes of Skyrim give you, there's a feeling the world in as immovable as a heavy rock. It never really changes anything, no matter what you do. TW3 on the other hand will gladly wipe out an entire village if you solve a quest in a certain way.

No, I have to disagree. A mini-game is a game within a game; for instance, an arcade machine or something similar where you can play space invaders. I don't think that true mini-games were introduced to GTA until San Andreas, though I don't remember which ones were added. The RC stuff would count as side-missions, in my opinion, as they take place in the same area where you move around, and you interact with the same 3d environment.

Okay - with your more-narrow than my own definition (to me, racing hobbyist remote-control cars in game is a "game within the game" but whatever) - as I recall, GTA IV has bars with pool tables where you can play pool, and arcade machines to play arcade games.

But again, that's IIRC - as it's been awhile since I've played GTA IV as well..

[Edit]: Perhaps this was one of them: QUB3D