The only times I notice the music in a restaurant are when it's really bad (Christmas music playing year round at Sichuan Cuisine), really out of place (Nine Inch Nails blaring out of the speakers at now-closed Tony Vallone joint Ciao Bello or Cannibal Corpse washing over the line of patrons at Amy's Ice Cream) or terrifically good.
The last category is far more difficult to find, as most restaurants focus -- rightly so -- on many other facets of the dining experience (the food, the service, keeping your water glass filled, etc.) ahead of the music. However, there are a handful of excellent exceptions to this rule.
5. Haven
In keeping with its locavore roots, chef Randy Evans's restaurant has an entirely Texan playlist, from Willie Nelson to Lyle Lovett. The only thing keeping it from being higher on the list is the fact that its portfolio of Texas artists could stand to be diversified: Let's hear some Selena or Lightnin' Hopkins, some Buddy Holly or Roy Orbison, some Toadies or even Polyphonic Spree. Texas has a great musical heritage aside from just country-and-western music.
4. Coppa
The excellent music selection is one of the first things I noticed about Coppa on my initial visit: Sam Cooke blended into The Black Keys, with the overall balance of the playlist heavy on classic Motown and old-school soul that matches the soulful cooking coming out of chef Brandi Key's kitchen.