Another idea you may wish to consider is the Walnut Room at Marshall Field's on State Street. The room dates to back to about 1907 and with Federated's insistance that Marshall Field's should be Macy's next year, who knows how much longer it will be possible to have this experience?
Teas are brewed loose, from Whittard's Teas (and Whittard's of Chelsea Teas are sold in the Gourmet Foods section in lower level of the store), sandwiches of chicken salad, egg salad, cucumber, and salmon, scones served with lemon curd, strawberry jam, and devonshire cream.