It is located in the quiet neighbourhood of Gamdevi, in a colonial house located on a street with many trees. The house belonged to Shri Revashankar Jagjeevan Jhaveri (long name) who was a friend of Gandhi and his host in Mumbai. It was his workplace between 1917 and 1934, and is now a house museum with photographs and everyday objects that belonged to Gandhi. The bedroom and living room are preserved, but can only be seen behind glass. There's an exhibition about the great man's life, made with models, and a large library of Gandhi-related books.
This used to be called the Prince of Wales Museum, and is still widely known by that name. This is one of India's major museums, celebrating the country's history, geography, and biodiversity. If you go to India, you need to visit it. Admission has apparently increased dramatically over the years, but it's still cheap, particularly if you have a student card (15 rupees I think). There are audio guides available at the door, although I didn't use one.