Your Shape: Fitness Evolved 2013 so you can impress the ladies. I suppose if I had to choose a game from that list then it would probably be NG. However, maybe you should ask for 60 dollar eshop points card. I'm sure there are a few decent titles on the eshop already and more to come soon (more games for the buck!).

Arkham City is one of the best games I've ever played, so there's my recommendation. There's more than a few nods to the design of Metroid and Zelda in there.

Sounds like Batman is the clear winner here. I did get to see a demo reel of it off of the Wii U station at Best Buy today, and it did look as good as other materials i've seen about it.

I'll have to talk to Smeags once he gets his hands on Epic Mickey 2.

Get Ninja Gaiden because it has Ayane.

Batman, because it has a large amount of Nintendo-ish game design and features simple, fun combat.

Ninja Gaiden is pretty much the opposite of those things. I would not touch any game in that series with a 50 meter pole.

Yours is a more compelling argument which i had forgotten: Ninja Gaiden is highly technical, which is a point against it compared to the more intuitive Batman

Batman it is then, unless someone can present good word of mouth about Epic Mickey.

I have not played Epic Mickey 2 on any system but I can answer you regarding the other two

Batman Arkham City

I have played the game on my PS3 and it is really awesome game with great narrative, decent melee combat, and really exceptional unique batman gameplay which is best part of the game. Unlike a shooter where you go area to area with new baddies to shoot in the head, in Batman games in each new room you have a new situation where you have armed and unarmed goons and you must do as batman would. Often there are also hostages to save so it encourages being stealthy for that reason as well as it is easier if goons stay unaware of your actions. The great thing is that it isn't a puzzle with one proper answer but rather a wide set of tools at your disposal and open ended solutions. It is very satisfying.

The Wii U version which I have also played adds some interesting use of the Gamepad. I know already I like getting separate sound from the Gamepad in addition to the multi-channel sound from my speaker system because that adds immersion. Being able to tap on the screen to detonate explosive gel is also good and using touch to work with "pause" menu can be more intuitive. The "pause" menu via Gamepad while you ignore the top screen or using the top screen in pause menus is just a change and doesn't streamline the gameplay better. It takes a little getting used to looking up and looking down.

The Gamepad+ points aside, the Wii U version of the game doesn't look as good as the PS3 version of the game. It's equivalent most of the time, but sometimes the bloom lighting is too much and textures are worse than PS3. There is no loading added, framerate is solid, but saving at checkpoints can sometimes stutter the game for a second or so. Maybe there will be some patch that addresses some of that but not currently

Ninja Gaiden 3 - Razor's Edge

They completely fixed everything that was wrong with the X360 / PS3 version of the game. It looks great and plays better. The best thing in my view is that the challenging AI from past Ninja Gaidens is back. You now have multiple weapons and an upgrade path. Lastly, it allows you to easily switch difficulty up or down between Hero (Easy) & Normal difficulties so that you don't get stuck on certain difficulty spikes that occur such as boss fights.

They took out the crappy competitive online mode from X360 / PS3 version of the game and added co-op mode similar to what was there in Ninja Gaiden 2.  It works great. The game also one of few Wii U launch games with SpotPass support.

Personally, I think it is the most stylistic Ninja Gaiden game to date and progression wise it is 2nd best. If you liked either 1st or 2nd game, this is for you. It's action gaming nirvana.

How about Mass Effect 3. Try something new Mr. Khan

Edit: I should answer the question though. Batman most likely. EM2 just added to the problems of the first game. The 3DS versions seems bit more interesting. Ninja Gaiden quality has gone down in the recent years. 

If you dont mind playing a game linear as hell. I would say you should play NG3.

Melee combat in Batman game works about the same as it does in Assassin's Creed games as in wait for them to attack, press the counter button then press the attack button. Rinse and Repeat. Where Batman shines is in the vast majority of game you play as Batman, using your gadgets, situational awareness, stealth, verticality and wide assortment of environmental factors to take out goons without getting into a mindless brawl.

Ninja Gaiden controls are very easy and satisfying. You can block everything that doesn't explode or grab you (which you can evade) and you have absolute command and advantage over the enemies when it comes to you going on offensive. You are very very powerful and deadly Ninja. The enemy AI is what makes the game challenging because they are relentless, brutal, work together, and will attack you anytime you have your guard down. The combat is very stylized and satisfying. Ninja Gaiden 3 - Razor's Edge keeps that awesome gameplay, while still making the game much more accessible and less frustrating than past games for less skilled players. For one thing, it checkpoints every single encounter so if you die, you don't have to re-tread since your last manual save point where were far apart in past Ninja Gaiden games. It also allows you to switch difficulty via pause menu at any time between Hero (Easy) and Normal. This just resets the game to last checkpoint with difficulty changed. There is meaningful Nintendo influence applied to Ninja Gaiden 3 design to make the game more accessible for more players without sacrificing what made the game appealing to its original core of fans.

Where Team Ninja went bad with Ninja Gaiden 3 on X360 / PS3 is that they dumbed their game down in order to appeal to broader audience, while Nintendo got them back to their great gameplay (even more stylized and enjoyable) while focusing them on smarter (and easier) choices of how to make the game less frustrating for players (checkpoints and change difficulty up/down easily).

Long story short

a) Don't pass up on Batman Arkham City regardless of console. Wii U is good enough with few + points and few - points

b) Give Ninja Gaiden 3 - Razor's Edge a chance, if what I describe is appealing or at least if they put a demo out. The game is fantastic for pure action game fans.