You want to do away with the hassle of the wire linking back to your computer, but have been advised against going wireless... but there is still one more option. Get a portable mp3 player and stick it in your pocket or somewhere on your person and then you can use wired headphones and still not be chained to your computer.
I recently purchased a pair of Yamaha RH5MA closed headphones for work. For a mere 45 bucks they put out a very solid sound with surprising tight bass. They don't leak at all, but unlike full-size closed cans, these sit on the ears with comfortable pads rather than around the ears, and being smaller they definitely look better for public spaces. Also they are low impedance so will work with most portable players I would think. I haven't had them long enough to give a detailed description of them, but they certainly sound much better than the Koss KTX Pros that they replaced.
That is just one headphone to consider, but that would still leave you one hundred bucks to buy a decent portable player if you want to try that route. I just have them hooked into my computer. They have a nice long cord for that so I can move around a bit. Also smaller headphones are better if you need to drop them down around your neck for example to take a phone call etc.
You said you wanted closed headphones to cut ambient noise, but still wanted to be able to hear people talking... I worked with a guy who used IEMs and he couldn't hear a dang thing said to him with those stuck in his ears, even if you were standing right behind him (which made it very handy to sneak up behind him and then scare the living daylights out of him). On the other hand, these Yamahas do cut the noise but not to the point of making it impossible to hear somebody talking to you (if you listen at an ear-friendly volume level anyway). Maybe the same is true for IEMs I don't know, but I admit I didn't like the ones I tried; what with the having to stick them in your ears and that they would lose all bass and sound quality if you bumped the wires causing them to lose their seal. I also have tried noise canceling - seemed like a gimmick that didn't really work...