Yes, new AKG K240 (Mk.II, Studio) and K271 (which AFAIK use the same drivers/shell, just closed back) are not a great deal for the money. I have a restored K240DF from ~1998 and it sounds much smoother. I also have the AKG K702 (modded) and given a proper amp (think Senn HD800 power requirements, so basically a power amp), there's plenty of bass, though not the Audeze kind.
Super cheap? Go Superlux - I had
the "HD-660" (not very known compared to other Superluxes), basically a Beyer DT660 ripoff - don't sound as good, but have a strong clamp, isolate well and the bass is not skull-breaking (however they're definitely bass-centric phones). On-ear, not over-ear. Mine (~2010) had incredibly good build quality, Beyer-level.
The ATH-M50, which I had the chance to directly compare against AKG K240 MkII, sounds similar to the AKG - the M50 has better bass and crisper highs, but K240 wins the midrange. The M50 are really overblown though, basically Beats level of popularity. Would go into some other AT closed phones at similar prices, like
ATH-A550Z - some people praise this line above anything else ($120/£140, welcome to Europe).
AKG K550 is also great, sounds more open than it looks and also isolates quite well, though I haven't heard any bass-heavy songs on them. Definitely more on the neutral side, but better bass than K240 at least.
Beyerdynamic DT770 could be a good choice as well (haven't heard them) if you like your sound more lowend-ish.
Going more "pro", I use
Senn HD280 for tracking due to their great isolation, but the clamping force is too strong for casual listening (IMO) and SQ is not great. Some people prefer the
Sony MDR-7506 instead (haven't heard them personally).
That's it I guess, have a listen to some of these if you can, google for "X vs Y" otherwise and see which sound signature you prefer. Hopefully it helps.
...
Really don't underestimate the try-for-yourself part - I wanted decent neutral portables, got the Senn HD25 after reading all the glorious reviews, and was very surprised with eardrum-piercing bass. Had to return them few days later, "burn in" didn't help either.