This is just 300 - 400m from Gateway of India.
The Taj Mahal Hotel at Colaba is one of the MUST see places because it has a great ambience and it is one of the most beautiful hotels in India. Also the 26/11 terrorist attacks happened here. This is very close to the Gateway of India. The harbour at this place looks great.
Right next to Gate way of India is Taj Palace Hotel, both the old and new buildings. Go visit Taj. It's an amazing architecture. A must visit is their Art gallery you'll get to know about the history of Taj Palace Hotel or if you're lucky enough you may meet a celebrity.