There are government as well as private medical colleges available in Mumbai 

There are 6 government colleges in Mumbai and they are

1) KEM college

2) Topiwala Medical College 

3) JJ Medical college 

4) Lokmanya Tilak Medical College 

5) Cooper college 

6) Rajiv Gandhi college 

And some other private colleges like 

1) Terna Medical college 

2) Somaiya Medical college 

Also a deemed university - MGM medical college 

The government medical colleges of Mumbai have cutoffs in the range of 535-545 and above. 

Students with marks in the range of 430-440 and above can take admission in private colleges as well. 

And deemed university accepts students with lesser marks but the fees are very high in the range of 20 lacs per annum. 

Hello!
List of the colleges accepting neet ug-
1. Grant Medical College and Sir JJ Group of Hospitals, Mumbai
2. Seth GS Medical College, Mumbai
3. Topiwala National Medical College and BYL Nair Charitable Hospital, Mumbai
4. Lokmanya Tilak Municipal Medical College, Sion, Mumbai
5. HBT Medical College and Dr RN Cooper Municipal Medical College and General Hospital, Mumbai
Check out the link below:
https://medicine.careers360.com/colleges/list-of-medical-colleges-in-mumbai-accepting-neet-ug