Maharashtra

The British Institutes is one of the best as they have qualified patience faculty and really good activities to help you get exposure to the language.

If I compare the three cities, Bangalore is the best option from them reason being:
1. Communication skills will improve.
2. IT Hub of India
3. 500 Forbes companies are there in Bangalore to explore different career options.
4. There are good colleges I.e. IIM, XIME, Christ University, etc.

For Pune: Go for SIBM, SCMHRD and BIMM
For Bangaluru: Christ University, XIME and IIM Bangaluru

Allinace, ABBS, SMU and Xaviers are the best institutions offering BBA in Bangalore. Check others below:
https://www.shiksha.com/bba/colleges/bba-bms-bbm-bbs-colleges-in-bangalore

IIT Bombay, Defense Institute of Advanced Technology, Indian Institute Of Aeronautical Engineering College, Priyadarshini College of Engineering are top colleges in Maharashtra, Annasaheb Danga College is good but not on the top.