Rome, classy as it generally is, doesn't really have much in the way of kitschy retro Rockabilly vintage bars in the way most big cities do.  Never fear, however, because these bars will still allow you to sip your champagne in a suitably vintage atmosphere.

Stravinskji Bar

Oh man, have you seen this place? Take a look at the link. Looking suspiciously like somewhere straight out of a Peroni commercial, The Stravinskji is a hotspot for the vintage hipster crowd of Rome.  Situated inside the Hotel de Russie, the beautiful outside garden terrace is full of wrought iron furniture, where you can relax and spot the beautiful people.  This is also a hotspot for famous actors and actresses. 

Although at 19 euros for a cocktail, maybe wait until we're feeling a bit flush.

Big Mama's

Recommended highly if you're a music fan, this little basement bar has been holding live music nights, especially those of the Jazz and Blues variety.  Vintage music fans should make sure to book a table in advance, as the place gets mega-crowded after 8. 

Low-key, fun and unpretentious, with a stage at floor-height, don't miss Big Mama's if you're a vintage music fan.

Cioccolata e Vino

I had to include this place in Rome, if only for the amazing CHOCOLATE SHOTS.  A very quirky little hidden-away bar that's well worth looking for.  All the shots are in Italian, and I won't ruin the surprise by telling you what they mean, but you may be in for a bit of a red face...
A beautiful, fun little vintage bar, and the only one I've seen like it in the world. 

Ice Club

Dress up in your best furs for this place! Costs 15 euros to get in, but that includes a cocktail that's served in a glass made of ice.  Worth visiting on a vintage-themed trip if only because it looks like it's straight out of an old James Bond film if it were set in Rome. 
Very friendly staff and patrons, generally.  You're liable to make a few new friends in here...

Casa Clementina 

Styled like a 60s abode in Rome, including a bed in the back room, all items are for sale, from the wine to the clothes hanging in the closet.  A very relaxed, but chic atmosphere - don't be fooled by the chilled atmosphere: dress to impress.