The record shops are pretty disappointing now, the best ones closed down in the last years.
On the contrary the live gigs/concerts scene is good, specially in summer.
Here's my favourites:
http://www.auditorium.com/
the main concert complex, nice to visit even if there aren't concerts at all if you're interested in modern architecture, Renzo Piano's work.
http://www.villaada.org/
A good place for 'world' music, situated in one of the city's parks, you can have a couscous, one beer (or two) while listening at music.
http://www.villacelimontanajazz.com/ita/programma_it.html
Same here, food, beer, but I prefer chilled white wine, some stupid roman ruines, and jazz concerts, lot's of young italian fellas in the program this year.