The Taj Mahal Palace Hotel is where the rich and famous stay when they come to town. If you can afford a night (or more) at this hotel so rich in history, opulence and city culture, you will be doing a disservice not to. Ask for a room with a view over the sea.
While I don’t usually recommend places right in the middle of the tourist areas, this is an exception. This hotel is a must see. Even if you don’t stay here, hang out in the lobby for a while soaking up their luxurious air conditioning while getting a much needed respite from chaos and the humidity outside!