On the second floor of the new Chicago Athletic Association Hotel, you’ll find the Game Room, a spacious playground for adults that draws a laid-back postwork crowd. The bar harks back to the building’s past as a men’s club, and the eight signature cocktails, created by (who else?) Paul McGee, skew classic. The best is simply dubbed Cup, and it combines rye whiskey, muddled lemon, ginger shrub, ginger beer, and angostura bitters. The pretty punch is a nice complement to your checkerboard-topped table, the ideal thing to hold in your free hand during a bocce match, and a joy to sip between turns on the billiards table (or bites of fried oysters). 12 S. Michigan Ave.