How To Play Wii Games On Wii U Without A TV

1. Go to settings.
2. Set video output to "no HDMI".
3. Boot up the WiiU and hold B so you get directly into Wii mode. Now the Gamepad is your "TV".

This works because the Wii U gamepad has a built-in sensor bar, so you don't need the Wii sensor bar.

Note: you still need a Wii-mote to play Wii games on Wii U. You can't use the Wii U gamepad or its controllers. As a result it seems more convenient to play Wii games on a Wii.

(Source)