Not like I wouldn't take any kind of 3D Mario game, because they're all great and some are the greatest thing known to man, but, I'm mostly still waiting for Mario 128.

And by that I mean, because I obviously know the real Mario 128 was cancelled/adapted into other things ages ago; a non-linear Mario 64 style game with plenty of stages with collectibles attainable in almost any order you wish, bound together by a cool, large hub-world filled with secrets .

But yeah, or Galaxy 3, or something new altogether. I'd take anything. They should call it 'Universe', whatever it is.

super mario Universe would have been perfect for Wii U. But at this point I hope it launches with the next Nintendo home console with amazing better than ps4 graphics

I would make it a successor to the more open Super Mario 64, though I would replace the melee attacks with Mario's hammer, so they could do things with it.
I don't really want a Galaxy 3. I think the novelty of having a spin attack wears off if you use an actual button by default.

A third of the people with Wii U's bought the game.  I kind of assumed that made it a success, brought down only by the small install base, and that Nintendo would continue with those types of games because they're easier and everyone still likes them.

Super Mario Universe. Or Galaxy 3, whatever. A follow up to Galaxy but with some design elements and sensibilities from Super Mario 3D World brought in, mainly in the form of alternate playable characters and power ups being supplemental rather than overly contextual.   And some 64 touches like a more nonlinear progression providing for more exploration oportunities. 

Or something totally new.

Another Galaxy or 3D World would be fine with me..

Galaxy sells like hotcakes so they should definitely go that way, especialy because they already have such amazing concepts in that series that can't be used in other kinds of Mario Games, think about Bee Mario, Spring Mario, Boo Mario and so on

I trust EAD Tokyo, they can do as they please.

I wouldn't mind slightly bigger and a few more epic levels, but I think SM3D World actually did a lot right. 

The power ups in 3D World are a lot better used than the ones in the Galaxy games too, and the Galaxy games have somewhat meandering design too. I went back and played Galaxy 2 and it's not actually head and shoulders above 3D World like some people make it out to be. 

Best case : SM64 successor / Super mario galxy 3.

acceptable: Super mario sunshine 2 / New concept

un-acceptable : SM3DW sequel

(if the next mario game for the NX, is a SM3DW sequel... there goes alot of my intrest in it)

I want an open world Mario game.

One big ass world you get to explore and unfold as you get deeper into the game. Every areas tightly designed to offer platforming bliss. As if the entire game was one single level. You start from Mushroom Kingdom and slowly and seemlessly make your way towards Bowser's Keep, with never a moment without platforming challenges. 

Could be hard to pull off. But if one developer can nail this, it's EAD, and I think they should try this approach at one point.