Doesn't You Tube have loads of music videos?
One thing you could do, since you have an iPad, is if it is a later model that has good Airplay, get yourself a cheap Apple TV box and you can Airplay videos across to the TV easily. I use Airplay all the time and it works amazing - as long as you don't have to mirror, so you will need an app that offers standard Airplay.
You Tube does and will Airplay at HD, as do plenty of other apps. So maybe you can find alternative iPad music video apps.