Yup..Rambagh Palace..no 2ways about it and somebody's gotta pa for your stay, unless you are rich yourself and can afford it.
Even though in comparative terms, prices are much less than what such heritage places would cost in something similar in say Europe.
Best is to get some conference organized there. One then gets to experience that place at reasonable prices, which doesn't pinch anybody. Go for the old wing rooms where each suite has a history - you are gonna sleep in the same bed that some royal backside graced till a few decades back.