I want to make a case for Saints Row IV: it is my go-to relaxing game. I have it installed on my PS4. The game has a GTA-esque setting and gameplay style, but where GTA is a clever satire of the real world, SR IV doesn't concern itself with the limits of reality: in fact, You play as the President of the US (with super-powers) and your main opponent is an alien overlord - with a pretty good voice actor. Now a lot of people tell me that SR III is the far better title and I bet it is, but if you haven't played the 4th installment I suggest you give it a try. It has a special feel to it that keeps me coming back. Not for the story, but for the happy accident that produced an almost meditative game. I love running through the city, killing aliens and causing all kinds of mayhem. Looking forward to hearing your thoughts on this title.
I think the fact that it doesn't have the same gravitas GTA has is part of the reason why it's so good.