Hello rajesh, from Mumbai you can go for JAI hind college that is a management school and is one of the best college from mumbai you can opt for or also you can go for St.xaviers college in mumbai or also podar college of commerce .. these are the top colleges for management studies in mumbai.. while in bangalore christ university or amity global university or ST.Joseph college of commerce these are one of the best colleges for doing bba. while, for doing bbm you can go for jain university or elz xaviers institute from bangalore.. but as you have mentioned you will be doing mba from abroad i suggest you to do bba from Bangalore as it will help you to get good college later in abroad.. 

all the best