A couple of headphone needs,

My son and his friends got Sony MDR-V6/7506 on my recommendation. Real bass a little crisp on top but great for monitoring and easy to drive via a DAP The only dig is they shock a little in extremely dry climate on a pile carpet. Use a little anti stat laundry spray. One can lasts 20 years.
I’ve had 2 pair for 30 years; the only wear is the earpads flake after 15 years, not affecting sound. Replacements are readily available.
Late night? I can't count the number of times I pulled them off thinking the sub was playing.

What is "inexpensive"? The Sennheiser HD 6XX from Drop at $220 are one of the best values out there IMO.

Depends on cheap is right. I like open-ear headphones like the Grado's, $125 to $2000. You might like them too since he'll be able to hear you or your wife yelling for him! But they lack the deep heavy bass kids (and others!) go for. My son has been using Bose due their excellent noise-reduction, and they actually sound very good. One factor is if possible to try them for their weight also, not just for their  sound quality. I got talked into another set of headphones that I never use due to the weight of them.

I used to hate headphones until I got the Meze Empy. It is fatigue free and I can listen for hours late at night (like right now). It is however $3K. Meze also make a headphone for $300 that is supposed to be real good, 99 Classics. Supposed to sound a bit like my Empy.

https://www.headamp.com/products/meze-99-classics?variant=28220732309568&msclkid=9b8e1ba8cf1c1ac...

Thanks.  I would want to spend less than 300 each. 

@whatjd ,

A word of caution. After much research I went ahead and bought the highly acclaimed PSB M4U headphones.

They were neutral and supposed to sound like loudspeakers etc.

Since then I've barely used them, preferring to use Koss Porta Pros / MK1 Sennheiser px100s or JVC flats. 

I've not heard the respected Sennheiser HD600s, or any of the Grado woodies, but naturally enough I'll be extra careful before shelling out anything like $300 for a set.

Comfort is a huge factor, and so is the question of open or closed back design.

The closed back PSBs aren't heavy but I like to almost forget that I'm wearing headphones. Can't ever do that with the PSBs. 

Generally open backed designs sound less boxed in and thus start off with a huge advantage. Whilst the PSBs might be good for a closed back design, they're having to play catch-up in many vital areas against open backed ones. 

Thanks for letting us know what your budget is.  I am a huge fan of the HD6XX and didn't type much last night as I was on my tablet.  The HD6XX besides being affordable are super comfortable, relatively easy to drive, sound great, and there are a lot of accessories available for them, things like earpads, different cables, etc.  Headphones in this price range often do one thing well, lots of bass, nice midrange, etc., but are often a one trick pony and don't do everything well.  The HD6XX aren't don't stand out in any one area, but are more of a jack of all trades, doing everything very competently.

I have about a dozen headphones, many of which cost much more than the HD6XX, including LCD-4, LCD-XC, Sony MDR-Z1R, Sennheiser, HD800, and Focal Elex, to name a few.  While these more expensive headphones do sound "better", I find myself reaching for the HD6XX often because of their comfort and while they may not be quite as good as the others, they come very close, do no wrong, and are very easy to listen to. 

I keep mine in my bedroom, as that is where I use headphones the most, often listening as I go to sleep.  The LCD6XX are the most comfortable set of headphones I have for this purpose.

I love my Drop/HIFIman HE4xx's that I got from Drop.com for $160. They have good detail, soundstage and nice fast bass and mids with smooth highs.

Another HIFIMAN fan here.  Not sure what kind of sound you prefer, but if “out-of-the-head,” open spatial imaging sounds attractive I’d recommend the HE400S, which is also easy enough to drive that it’ll work using a cellphone but good enough that it’ll scale with a better amp/DAC.  A good deal can be had on Amazon by choosing the “Like New” option sold by Gramophone for $160, which is what I did trusting their highly favorable reviews, and they’re great — truly like new at a good discount.  If you prefer a little more intimate and tonally richer experience then the Sennheiser HD6XX would probably be a great option — just depends what you’re looking for. Hope this helps, and best of luck. 

Thanks to all.  My two main sources for music are my own CD/SACD collection and two very good college/public radio stations.....mainly listen to classic Jazz from the 40s through the 70s and  female vocals.