Wow, rather large budget I see. Okay, for your price ranges I've got 2 options with different qualities for both of your price ranges so you can pick the one you feel is better suited for your friend.

$800 Budget

Option 1: Audez'e LCD-2 ($825)
Alright, for a mid-forward signature and a great thick sound that's perfect for hip-hop, nothing beats this headphone at the sub-$1,000 price range. It has a warm, detailed, and punchy sound that's also a favorite amongst mixers and sound engineers. The mids are the real sweet spot on these headphones, sporting some of the best in any set in the world, minus Stax and the upgraded LCD-3. They've got very rich and lifelike tonal balance which stays true to the real world. Everything is fantastic throughout the whole sound spectrum, though. It's a very well regarded set by the Head-Fi community, and is actually ranked as the community's overall favorite headphone. In my opinion, its big, retro wooden look is a huge plus for me, though I don't think he would want to be wearing it out on the street (although, other audiophile will definitely notice them from a mile away). Another thing about this option is that it doesn't fit the closed-back preference - it's a semi-opened back set and isn't too suitable for outdoor use. It won't isolate a lot, and leaks a little sound. If its bearable, this is the #1 option for this price range (It might run you a little over $800). If not, I'll have to point you towards the Audio Technica ATH-W1000X.

Pros: Very balanced sound across the spectrum, thick/warm and punchy sound, sexy wooden look, can be driven by an iPhone (as claimed by Audez'e), reference class headphones, true to life sound, godly mids
Cons: Price, open-backed

Option 2: Audio Technica ATH-W1000X ($675) - Now this here is one of my personal favorites. Audio Technica is really known (and this set in particular) for their bright, clear treble, punchy bass, and a V-shaped sound signature. Now because the bass and treble are emphasized over the mids does not make the mids bad. The mids still remain natural and lifelike, and with some EQ to reduce the bass, the mids really shine on these headphones. These are great for bass-heavy music and vocal music; dubstep, drum n bass, hip-hop, rap, etc. but I wouldn't recommend them for rock as the bass is too prominent and the sound isn't as aggressive as one might like for rock. These should run you around $600-$700 MSRP.

Pros: Punchy with good bass extension, laid-back sound, clarity in trebles, amazing wooden look
Cons: Shy mids, might need amplification

$200-400 Budget

Option 1: Audio Technica ATH-A900X ($230) - Another candidate by Audio Technica here, this is also much representative of Audio Technica's house sound that I mentioned in the above paragraph - though, the sound is more balanced out and less colored throughout the whole spectrum, which is all personal preference. The A-series by Audio Technica is also renowned for its above average soundstage which makes it very suitable for recordings at live concerts, classical, video games and movies alike. This is a really promising set that's on the lower end of your price range, but high end on the sound side.

Pros: Powerful and deep bass, clarity in trebles, very comfortable, very good soundstage, closed-back
Cons: Recessed (but lifelike) mids

Option 2: AKG K701 ($275) - These are another legendary set produced by AKG, which is one of the best - and not just at its price point - headphones in regards of midrange, and especially soundstage. The overall sound signature does not provide much punch to its bass, but has a great mid-forward sound complemented by nice treble. Now, these have a couple downsides based on your personal preferences, and it includes extreme need for amping, as as mentioned, weaker bass. It's also open-back, but if he's going to be using these mostly for home, and can get these to work with a decent $150 amp whicthese would be spectacular.

Pros: Amazing soundstage, fantastic mids and trebles, iconic look (featured in quite a few animes)
Cons: Shy but deep bass, requires powerful amp, open-backed

Hope this helped you man, best of luck pairing your friend up with the perfect set.