My favorite are my Stax 009s, however, you won’t find them around $1,000. There are better headphones out there, but again you won’t find them around $1,000. For that amount, I suggest you look into the Audeze line. I bought a pair of LCD-XC to see how closed-back phones might sound. They sound very good, although a bit heavy in the weight. I see lots of Audeze LCD-X at around $1K, and I think you could do a lot worse for your thousand dollars. Just my two cents. You might also try a used pair of Sennheiser 800 (800S, if you get lucky).
I just re-read your post, and realize your budget is "greater than" $1,000. In that case, I recommend Focal Utopia (on my shopping list too), RAAL, and the current top of the Abyss line. Also, be sure to get a dedicated headphone amp worthy of your initial investment (Blue Hawaii comes to mind). By all means, try to attend a Hi-Fi show to help you make the right decision.