If you look at Elliott's name plate the lettering is in the style of the series credits.The name of the theatre is the Woolcott. Alexander Wollcott was a critic back in the 30s, 40s and 50s.
The episode allegedly takes place in NYC (i.e. Broadway, New York Chronicle), but the theater used for the exterior shots is the Ricardo Montalban Theater (formerly the Huntington Hartford). It is clearly located in Los Angeles, CA as evidenced by the stars in the pavement, which is the Hollywood Walk of Fame.
Rich Little's character says that he has an ability to mimic the writing styles of various critics. Little is a professional impressionist, performing impressions of, among others, every U.S. president since Kennedy and several celebrities.
The photographs on the wall in Lt. Jarvis' office are that of then-Gov. Mario Cuomo and then-Mayor Ed Koch.