Some distance west of the Park Hyatt you also have an alternative in the Opera City cultural complex/skyscraper. You can enjoy a classical concert in their two concert halls and have a meal or just a drink before or after either in the downstairs shopping/dining mall or the ten or so panorama restaurants on the 53rd and 54th floors. Prices are somewhat more moderate than at the PH.

Link: http://www.operacity.jp/en/index2.html

Otherwise Shibuya and especially Omotesando might offer more stylish surroundings for an evening stroll. It's a Paris meets Milan meets LA and a glimpse of future kind of place.