(I realise that this may not help the OP, but the next person looking for information may benefit)

I grew up in Mumbai. My personal recommendation would be to stay further south and commute northwards during the day when touring. South Mumbai is the old business district, BKC just south of the airport in Bandra East is the "newer" business district. Most people stay in the northern part of the city, because it's cheaper, and commute southwards. Going against the traffic is usually a better experience. The local train service is fantastic, but you definitely do not want to deal with the crowds of daily commuters going to work. Going north/south in Mumbai by road isn't usually a good idea.

South Mumbai is usually older classics, Bandra West is the slightly more hipster area.

Food wise, I would strongly suggest looking for places serving cuisines you may not be familiar with (in addition to the recommendations above). Jimmy Boy ( https://www.jimmyboy.in/ ), Britannia or SodaBottleOpenerWala for Parsi cuisine. The Tanjore Tiffin Room for Chettinaad. O Pedro in BKC for Goan. Shree Thaker Bhojanalay for a proper Gujarati thali. Maaslli Saraswat and GSB speciality for GSB cuisine.

For interesting sweet snacks, I like the offerings at Bombay Sweet Shop in Bandra (their bhel chikki is a lovely snack, and isn't available elsewhere). Chitale Bandhu Bakarwadi is a known classic. You already know of vada pav, there's also pav bhaji (a vegetarian sloppy joe).

If you arrive during the Ramzan/Ramadan season, Muhammad Ali road is a lovely place for a food walk after sunset.

And in lesser known attractions, the railway museum at CST is worth a visit https://shop.museumsofindia.org/node/287