This restaurant is known for its Korean fried chicken and it's classic decor. The Prince's red leather booths, wood paneling and classic wallpaper make it popular for filming period pieces, or just a good bar scene.
Nick is a bartender at The Prince.
Don Draper drinks in The Prince's red leather booths in episode 1x02 "Ladies Room".
Source: I Am Not a Stalker
From episode 1x10 "Los Angeles".
The Mitchum brothers take Dougie out to celebrate after not killing him in episode 1x11 "Part 11".
Nick Naylor (Aaron Eckhart) dines with Bobby and Polly.