CSMVS Museum
The Chhatrapati Shivaji Maharaj Vastu Sangrahalaya (still widely called by its old name, the Prince of Wales Museum) is Mumbai's finest, set in a domed Indo-Saracenic building of 1922 among palms and lawns near the Gateway. Its galleries run from Indus Valley seals and Gupta sculpture to Mughal miniatures and a room of European painting.
The foreigner ticket includes an audio guide, which is the easy way to make sense of the collection; two or three hours is about right. It's open daily and within walking distance of the Gateway and Colaba, so it slots neatly into a day downtown.
Mumbai's great museum
