Recommend Travel Headphones, wireless, closed back, under $500msrp

I use Bose Quiet Comfort SC - decent sound, rechargeable, comfortable with excellent noise cancellation.  We bough one pair in hard case on Amazon and the other in soft case in Costco ($329).  Identical, other than the case.  Soft case is flimsy, but smaller and sufficient.  It is wireless, but also comes with cable for direct connection.  There might be many headphones better sounding than Bose, but not many that cut noise that well.  When engine noise gets thru on the plane sound quality becomes a little bit less important.

Great question. It took me decades of carrying around extra DACs, and battery powered head amps, and in ear phones. Also, CD players. Honestly for travel. My choice is Bose QuietComfort Ultra Headphones. In high noise areas like virtually all travel, you cannot create an audiophile experience. All the fine details get lost. You need somthing that is built for noisy environment (with good noise cancellations) and the Bose are probably the bet.

Also, there are these. But the Sony are a bit analytical.

Sony WH-1000XM6 and Sennheiser Momentum 4 Wireless also worth considering. 

When I get to the airport I put them on with noise cancelling only and take them off when I get to where I am going. I have flown and traveled for hundreds of thousands of miles with them. I would never go anywhere without them. Supremely comfortable!

I use the Bose (over-the-ears) as well. The ones I’ve got I’ve had for probably 6 or 7 years. The charge lasts a looong time and they sound great. In fact, I sometimes have to take them off to make sure nobody else can hear them. I usually watch a movie or two on the plane and I’m very happy with them. They’re also super comfy as well. I’m generally not a huge Bose fan but I would certainly recommend their headphones. 

I have owned and enjoyed the Bose, but now have and prefer the noise cancelling of the Sony WH 1000 XM6.  Probably cant go wrong with either and for airplanes don't need to spend more.  The Sony Noise cancelling is cool in that when you talk to someone the NC turns off.