Honestly, once you hit about the $100 mark, most of the "studio headphones" have a flat enough frequency response to mix on...
I've actually found that this, in my experience, is not the case. I've purchased a number of different pairs of AKG and Sony headphones, looking for something close to what OP is asking for, and I've found that in the $120-$150 range, AKG headphones can sound very different, based on drivers, headphone casing design, etc.
The AKG K271 mkii headphones linked below reproduce audio pretty close to what I would expect it to sound like when I, say, plug it into an iPod or some such device and listen with no EQ setting enabled:
Amazon.com: AKG K271MKII Closed Back Circumaural Headphones: Electronics
Conversely, these semi-open backed AKG's are very different "sounding" - probably flatter than the closed-backs above, but they are also pretty lifeless-sounding. They work for me for mic placement on acoustic guitars since they seem to more accurately reproduce mid-range without any excess bass or high-end. While that may sound like a great characteristic, they are also crap for even casual headphone-based mixing since you don't get a good feel for the low-end:
Amazon.com: AKG K240MKII - AKG STUDIO STANDARD SEMI OPEN 55OHM HP: Home Audio & Theater
They don't sound "thin" - they just sound like they have a hyped lower mid-range, so you don't feel the bass as much. May be due to the semi-open design, I don't know.
All in all, I'd probably recommend the closed-backs, but I also don't think you're going to find a golden pair that will do everything you need, unfortunately. If you do, let us know - I'm sure plenty of us have been looking for the elusive "perfect pair" for a long time...