there are some sites with free games on like
http://www.wiiarcade.com/ which can be fun and a bit different if you are bored with the games you have.
browsing the web is ball achingly slow as you have to pick the letters to type in your searches and addresses
zooming round the world getting the weather is amusing first time you do it
my daughter loves the virtual console - she had been thinking of getting a 2nd hand n64 and a copy of pokemon snap - then she found it on virtual console downloaded it and was playing it immediately
Overall i'm not sure I'd go out and get a wireless router just for your wii, but if you have a router you'd be daft not to use it