I'm just hoping for an SSE style Adventure Mode on Wii U, with no story (as it's been deconfirmed, though I would have liked a returning story), and levels themed after Nintendo franchises (as well as represented third parties, such as Mega Man and Sonic), with some boss fights.
The levels could also have a bigger degree of exploration in general, since Smash Run on 3DS is already a gigantic map similar to the Great Maze, but they'd still be a "get to the end" affair, just with a few hidden areas and alternate routes. Also, two-player co-op locally, and four player co-op online. Locally, one player uses the TV screen while the other uses the GamePad. In online, everyone just has their own screen.
Even just basing the levels off of existing stages in the regular game would suffice, and would be easier, as they could re-use assets. And of course, Smash Run already has plenty of enemies to work with (who likely have models in the Wii U version for trophies).
Also, this is REALLY wishful thinking, but wouldn't it be really cool if the World Map was like the one in Super Mario 3D World? Obviously, the levels themselves would be side-scrolling, but I think a World Map system similar to Super Mario 3D World would be really charming in Smash Bros. Just imagine playing online with four players, and seeing Mario, Link, Samus, and Kirby, or any group of characters, just marching around this 3D World Map in a line, and having little secret areas to find. Heck, I'm pretty sure Nintendo EAD would let them use the code and what not as a base for it.
Also, I think to help expand the overall scale of the map without having to make more than 30 - 40 odd levels (which I think would be an ideal amount. SSE had about 30, IIRC), they could make Event Mode from previous games a part of this Adventure Mode, with events having their own spaces on the map. Events would still take place on the normal stages from multiplayer, though, and would focus strictly on fighting other characters. The bigger Nintendo franchises like Mario and Zelda could also have multiple levels based on different games in their franchise (for example, Mario could have a Mario Galaxy stage, a retro themed stage, a Mario Kart stage, and a stage based on another one of his 3D games).
The party system from SSE could also return, though it's not necessary. They could also bring back the sticker system, or implement something similar to Smash Run, except the upgrades are permanent, and they are more scarce.
If the Wii U version had a mode like this, E3 would be the time to reveal it, and it would get people really excited, I feel. Unless it's just me, of course. :I