O.K. Are you a 'depends on the source/recording person'? I am the like that mostly, CDs for now.
How the music is presented and makes you feel: close, less close (first two: intimate), small distance, moderate distance, etcetera... Do you favour a more weighty low end and good mids and highs or do you prefer more mids with less emphasis on the lows and highs? In short: how do you like to hear your music?
According to some the Grado SR60, otherwise SR80 is one of the best sounding headphones but not closed. Since you prefer closed without amplifier a Shure SRH440 or Sennheiser HD448 could work too. And that is just the start so check out some reviews and ask around on Head-Fi... Audio Technica, Denon, Beyerdynamic, AKG, Sony, Pioneer and Koss are just a few brands with possibly suitable headphones.
I can tell you that if there is one headphone I can live with if I had to choose one for unamplified indoors use it would be my Sennheiser PX200 II. It does pretty much everything right and sounds good too. Number two for now is the AKG K181 which sounds better than I ever expected.