Travel headphones need to be...

I'm in research for the best to my needs headphones which is narrowing my search to:
maximum comfort
portable and foldable
no earbuds or in-ear = minimum comfort = unacceptable
performance clarity natural
ipod friendly(but not necessary plan to buy portable amp anyways)
budget $100 or bellow.
I second the Sennheiser PX-100. Great with the iPod, even better with a portable amp.
I agree with all the posts so far - they are good sounding ones, but I stopped listening to headphones, 'cause Doctors are saying they ruin your hearing...
I would recommend trying a small powered speakers to travel with, like audioengine a2 speakers.
I guess travel headphones should be noise cancelling, so AirPods won't suit noisy trips I guess. I don't know what design you prefer, but different travel blogs confirm that  MonoDeal headphones are perfect for travelling (the price is rather loyal, about 40-50$ ).