ROCK BAND.

Mario Party 8 comes to mind, but that's just a big fat collection of mini games, so probably not. heh.  The board game theme is neat though.

The original Final Fantasy Chrystal Chronicles for the Gamecube is compatible with the wii, i think?  Haven't played it though.

We have Endless Ocean and have a lot of fun playing it. My 6-yr old loves to discover new creatures and find little treasures. It's only single player, though. Thru Wifi you can dive with a friend.

I know you said you don't want minigames, but Carnival games is pretty fun. Give it a rent to see if you like it. Also, you mentioned not wanting a Mario Game, but Super Mario Galaxy is pretty fun because you can control Mario, while someone on the second wiimote can grab stars and use the stars to shoot the monsters. Perfect for a younger player to join in, yet not essential to the game.

Any interest in golfing games? Super Swing Golf Season 2 is fun. They made some improvements and made it easier for the novice player, most importantly allowing newbs access to the set of clubs that give you a perfect shot every time.

Ours doesn't take that long to load. Usually just after the diver drops down below the screen, I can hit the A button and start the dive. Are you letting it just run without hitting the A button perhaps?

It must be the piece of crap disk I got from Gameflop.  I press every button during the waiting times and still get up to 80 or 90-mississippi before things start happening again.

Cooking Mama.
Dance Dance Revolution. 
Ninja Reflex.