Alliance

In Bangalore you should give first preference to Christ University for BBA, if not you can consider Alliance University. There are many Bangalore University affiliated colleges, also Mount Carmel (only for girls) (Autonomous), St Josephs, Kristu Jayanti, Presidency, etc. But still Alliance is on the path of success and gaining market value. This is the best university in India for BBA, the teachers are so good that you would learn everything in three years and there is no need to do MBA too, until you need an additional certificate. I accept that the college is located in a village, but Anekal is slowly developing. The environment around the college is so good, that you should not have a second thought of joining here.

MIT Arts, Commerce and Science College and Alliance School of Business are equally good. Some of the important points while selecting an institute - Accreditation of the institute, institute's infrastructure, teaching faculty, specialization offered, past placements records., tuition fees, city preference and industry interface. As both the institutes are having the campus in Bangalore and Pune. Industry exposure is good for students in either of the college. If possible a visit to college is better option to get a reality check. Also, get in touch with college alumni's through the social network to get information about the latest changes if any.
You can compare the course fee, placements, students review, facilities offered and seats-
https://www.shiksha.com/resources/college-comparison-170945-147327