The Parel/Worli area (where the FS, St Regis and Grand Central are located) is the former industrial core of the city, which has now been repurposed/redeveloped as a CBD and nightlife district with some great food and drink options (reservations recommended for most of the upmarket higher rated places). However, as a tourist, you will be closer to "old" Mumbai at the Taj Mahal Palace and Towers.

While a bit away from the center, Bandra has a number of things to see and do (including some of the top food options in the the city) but only one large luxury hotels, ie. the Taj Lands End, which is a bit dated but still very decent.