I used to carry around Sony V6, because they were closed and had plenty of bass for when I listen to rap to get pumped up for sports/workout, but they were a pain to carry around, even in a backpack. The V6 folds into a box-like shape, whereas Grados can lay flat. I would never wear it around my neck simply because it would be too uncomfortable.
I use Shure E2C right now they are fine for classical but I cannot listen to rap with them because while they have more bass compared to other canalphones, they have none in comparison to full sized cans. My broken ksc-55 should be coming back in the mail from Koss, and I'll use those for rap. I asked for the replacement to be ksc-75 I wonder if they will do it, they carry the same retail price. Koss 60ohm headphones may be a good, portable option. So are Sony V6 if you don't mind the bulk.