IIT Bombay has one of the best views. Not many people know about it. You must take a photo from the institute top from where the Powai lake is visible.
Mumbai is captivating, it depends on the kind of Photography you are interested in. For street photography - Colaba, Bandra and Dadar.
For Night Photography - Marine Drive, Worli Seaface, Bandra Bandstand, Gateway of India, Haji Ali
I assume the answer to this question is 'almost the entire Mumbai' if you have the time. When you visit a city for the first time, everything about is a must see.
Marine Drives ,Gateway of India,Juhu Beach,Aksa Beach,Churchgate,CST,Hanging Gardens everything its a stunning city and you can capture hell lot of stuff
I will suggest that you should opt for a Heritage walk in Mumbai. Check out www.bookmyshow.com They take you all famous / unexplored places of Mumbai which give very good photography opportunity . Also there are specific photo trip as well . Eg as of now you can go for a photo trip to Sewri to click pink migratory flamingos .
Sanjay Gandhi National park Nariman point
Shivaji Maharaj museum
eliphanta caves gateway of India 100 km away from Mumbai Much more places which is best for the solo travel
like 1)Ali bagh {khim beach,kashid beach and forts.}.
2) Lonavala {Karla caves , view point ,ek Vira mandir and bhusi dam)
3 ) Igatpuri 4) sandhan valley, kolshubhai peak ,bhandarda etc