This proves that the router is the problem.

What model is it?   If its a generic ISP router that might be the reason.



EDIT:

People with Nintendo devices  or tablets and smartphoned that have router problems should try to give those devices static IPs.

Not just normal static IPs but let the router find the device and check for its MAC adress and based on that give a static IP. (so you dont have to change the devices internet settings all the time when visiting other peoples houses and trying to access their internet)

This works quite well  because a ton of cheaper routers  go nuts when there is more than 3 or so devices that want to have IPs.  "static" MAC based adresses avoid this.

The WiiU Wifi does seem to be a little temperamental, my brother's was having connection issues even though other devices were fine in the same location.

You could try moving your router and Wii U closer to each other to see if it makes any difference. Another thing would be changing the channel that your router uses. People in built up areas can get interference from neighboring Wifi sources, changing channel is a pretty easy way of minimising interference.

I haven't had any problems with the internet connection, and I've tried it at three different locations/setups.

How does it prove the router is the problem? When I take the WiiU closer to the router there are no issues. My ps3 gets a low signal too in the same spot but still works. The wi-fi receiver in the WiiU is the weakest of all the devices I have.

I have a Linksys wrt610n router btw.

Internet connection's fine, but my WiiU just locks up a lot. Seriously, like 1/3 of the times I play it.