I like a tuneful, analog type bass. Bass that is slightly "under" rather than "over" damped by the amp, analog vs digital type of bass response. It doesn't have to plumb the deepest depths either and I can live without the kickdrum to the chest and pants flapping. When it comes to midrange, I like a pure midrange but it can't be leaner than reality. I'd rather have it tilt the other way to add some extra meat on the bones and chestiness but never lean.
Tweeter response is the one aspect that can absolutely kill it for me... I don't ever want to live with a tweeter that has audible distortions, break up or non linearities. I can not hear past 15Khz which is pretty typical for a guy in his 50s but man can I still hear that annoying metal dome tweeter flavor that sounds worse than a dentist drill... I strongly prefer the silk dome or similar to a metal dome tweeter that offers tons of perceived air but sounds nasty with anything but a perfect recording.
In a nutshell, I am not a recording engineer, I am not trying to master an album. I am into enjoying music. It doesn't have to be perfect... It has to be engaging, intoxicating and seductive when appropriate. If the system errs on the side of warmth and humanity, so be it. My choice of Luxman Class A and Harbeth speakers are a testament to that.