If they want a scene, then the Martini Park sounds like the right call. But if they're into classic cocktails and concoctions, nothing, at least in my mind and at this point, beats the Violet Hour. Great noshes as well (chorizo croquetas, deviled eggs).
My favorite swank cocktail experience in Chicago is the bar at the Peninsula Hotel.
If they're interested in getting off the beaten path, Weegee's is a great slightly hipster westside neighborhood bar where they take their cocktails damn seriously. Thoughtful and precise.
Of course, the old reliable is the Matchbox. Great personality as well as being able to mix super cocktails.
Lately, I've been enjoying Friday happy hour (5-7) at the Green Mill with Hammond organist Chris foreman. The room is one of the best in the city and Foreman keeps the usually small crowd happy. No cover.
Violet Hour
1520 N Damen Ave
(773) 252-1500
Weegee's
3659 W. Armitage Ave.
(773) 384-0707
Peninsula Hotel Bar
108 E Superior St
(312) 337-2888
The Matchbox
770 N Milwaukee Ave
(312) 666-9292
Green Mill
4802 N Broadway St
(773) 878-5552