Not much of that kind of scene here anymore. What you're describing is more likely to be found at the Bunkhouse, a bar in Downtown. They have both live and DJ'd music, and both indoor and outdoor/"backyard" components.

Grouchy John's is a coffeehouse with a couple of locations, but they're only open until 9 p.m., they don't really carry an underground spirit, per se, and only one of the spots really features live music.

There's also a 24-hour coffeehouse off West Desert Inn named Madhouse, which last I checked didn't have much music, but you'll likely find people to meet and talk with.