I received the system from Amazon last night and bought Super Mario 3D World from GameStop. Getting it to connect to my wifi was a huge hurdle, and the lack of an ethernet port is an outright dumb omission. After looking for help online I found that I had to manually configure the wifi connection which completely undermines Nintendo's philosophy of making their platform and games approachable for everyone. Not only that, but the network card is apparently a piece of shit because I have to have the Wii U in the same room as the router in order to hold a connection. So... online is a no-go with this machine for me.
I didn't have much time to play Mario after fucking around with the wifi settings and waiting for the system to update, but so far I'm really disappointed in the hardware.
I am always a little puzzled when I hear about people having network problems with their WiiUís. Maybe I just got lucky but I have never had trouble getting them to sync up instantly, even when Iíve brought it to other peopleís houses. My router also has two walls between it and the console so Iím not sure why distance is a problem for you unless you live in a lead bunker.
One thing I have noticed is that Nintendo devices (3DS as well) donít like the WPA+WPA2 setting on routers. Have you checked your settings? It might be as simple as switching to just WPA.
Unfortunately, the System Patch is pretty essential if you donít want to have a miserable time with your WiiU so getting internet is important.