Here's a fun fact relating to your newly purchased Wii U console: the Nintendo Network account that you created on it is locked now to that console. This means that you can't sign into your account from another user's console and that if your Wii U is lost, stolen, or replaced for one reason or another, you'll be creating a new account for yourself.
Nintendo's support page suggests that this won't be a forever situation, at least with regards to accessing your account from other devices. "In the future, you will be able to use your Nintendo Network Account with future Nintendo consoles and other devices, such as PCs," the support page reads. Up to 12 Nintendo Network IDs can be registered per console, but for now they'll have to live there and only there.
This of course raises question of what happens to your owned licenses for digital content should your Wii U need to be replaced for one reason or another. We've checked in with Nintendo on this; stay tuned for more info as soon as we hear it.