Alright, I've been getting so much mixed feedback I thought I'd start from scratch again.
Budget: $200-$250 + 150 for amp
Source: Lenovo Y50 and Galaxy S6 running through an amp, DAC to come in the future.
Music: Classic rock, a lot of Springsteen, U2, and the such
Isolation: Doesn't matter, will be used entirely at home, so I don't need it, but I wouldn't turn it down.
Type of sound/what I'm looking for: I'm looking for a neutral headphone. If a song is bass heavy (which very that I listen to are) I'd like to hear that bass, but I don't want it to be overpowering. I'd like a good soundstage and to be able to pick out the instruments. Springsteen has a really big and complex sound now with many horn players and backup singers. I'd like to hear the details without it being analytical and cold, if that makes sense. I currently have a pair of Westone W10s and I like the sound it has. I'd like a wider stage and a little more detail.  
I will say I like the visual style of AKGs but I'm open to other brands.  I also need the cables to be removable.
Thanks for all of the help, and let me know if you have any questions.

What about Massdrop's AKG K7XX?

I think the AKG K712 is probably better than the K7xx, but that's my opinion, obviously.  I have an original, low-serial-number K701 and have owned the Q701 as well.  The K712 is a superior phone.
 
That said, I would still recommend the Sennheiser HD580/600/650 family first.  Unfortunately, it sounds like one of those is a bit out of your price range - but not by much.