Engineering in Mumbai

IIT Mumbai offers a course in Aeronautical engineering. It's probably the best college to offer any course. However, there are many other good colleges which include VJTI, Indian Aerospace and Engineering, Thakur Institute of Aviation technology etc. that offer such courses.
Refer to the given link,

Hello,
Admissions to all colleges in Maharashtra is based on MHTCET and neither on JEE Mains nor on marks obtained in 12th. You will have to appear in MHTCET if you want to get admission in any college of Mumbai.

Hello Anjali,
For admissions in engineering colleges in Maharashtra, you have to appear for MHTCET but normally seats are reserved only for domiciles of Maharashtra. However, you can get admission from management quota of private colleges.

Hello Rajesh,
Indian Aerospace and Engineering is an institute, which is actually not an engineering college, but an institute that trains in aircraft maintenance that is approved by DGCA.
You can check the below mentioned link:
http://www.iaemumbai.com/

Some good medical colleges are :-
Seth GS Medical College and KEM Hospital
Topiwala National Medical College
Grant Medical College
Padmashree Dr DY Patil Dental College and Hospital
Terna Medical College
Rajiv Gandhi Medical College
Mahatma Gandhi Medical College
Good colleges for engineering in Mumbai are:

IIT, Mumbai is the best college to pursue mechanical engineering.