As you have asked about the best time and places to visit Mumbai, I am giving you information about it, check below for the details
The best time to visit Mumbai is from October to March.
These months are also ideal to enjoy a stroll around marine drive.
The weather remains cool and dry.
The day temperatures remain pleasant in the range of 28°Cto 33°C.
The minimum temperature drops down to 10°C.
This time is perfect for sightseeing and other tourist activities.

Places to visit in Mumbai:

Gateway of India
Chhatrapati Shivaji Terminus
Siddhivinayak Temple, Mumbai
Girgaum Chowpatty
EsselWorld
Sanjay Gandhi National Park
Haji Ali Dargah
Elephanta Caves
Babulnath
Chhatrapati Shivaji Maharaj Vastu Sangrahalaya
Kanheri Caves
Elephanta Island
Bombay High Court
Jehangir Art Gallery
JW Marriott Mumbai
Temple for the city's patron goddess
Kamala Nehru Park, Mumbai
Mahalakshmi Temple, Mumbai
Horniman Circle Gardens
Mount Mary Church, Bandra
Dr. Bhau Daji Lad Museum
Worli Fort
Taraporewala Aquarium
Walkeshwar Temple
Jijamata Udyaan
Powai Lake
Regal Cinema
Global Vipassana Pagoda
Nehru Science Centre
Shivaji Park
Aksa Beach
Banganga Tank
Mahakali Caves
Marvé Beach
Rajabai Clock Tower
INS Vikrant
Castella de Aguada
Cathedral of the Holy Name, Mumbai
Knesset Eliyahoo
Synagogue
Wankhede Stadium
Brabourne Stadium
Vihar Lake
Mahalaxmi Racecourse
Afghan Church
Jama Mosque, Mumbai
Nehru Centre
Madh Fort
Metro Big Cinemas