Hey aspirant ,
Top colleges for BBA in pune are

1. MIT World peace University , Pune

2. Tilak Maharashtra vidyapeeth , Pune

3. Symbiosis institute of computer studies and research , Pune

4.Bharati Vidyapeeth institute of  management and entrepreneurship , Pune

5. Ajeenkya DY Patil University , PUNE

Hope this helps , all the best .