I think Orchard Road is the last place you'd want to be if your goal is to get away from the commotion of tourist restaurants and shopping malls.

I can think of two general options. Get as far away from the city center as possible for a hotel near a nature reserve. Maybe something around the Changi area like http://raintr33hotel.com/. The alternative might be one of the colonial style hotels in Singapore that, although they aren't surrounded by nature, still have an atmosphere of escapism created by their architecture. The Raffles Hotel and the Fullterton are two examples I can think of here. The Raffles has some beautiful interior courtyards.