Gandhinagar

Best colleges for BBA in Finance in Ahmedabad and Gandhinagar are:
-School of Liberal Studies, Pandit Deendayal Petroleum, Gandhinagar
-Neesa Institute of Management Studies, Gandhinagar
-Gujarat University, Ahmedabad
-Unitedworld School of Business, Karnavati University, Ahmedabad
-GLS (J. P. Shah) Institute of Business Administration, Ahmedabad
-L J Institute of Business Administration, Ahmedabad.

Old IITs are the best. They enhance your personality.

I don't think that is possible for engineering colleges in India. You will have to start from the first year in any college that you chose to admission in.

IIT Dhanbad or IIT Hyderabad will be more better. I will say IIT Dhanbad.

Computer Engineering course in PDPU was started first time in August 2016. so, you can study CSE from PDPU Gandhinagar. You can refer the following link for the details about the admission process at PDPU
https://www.shiksha.com/b-tech/course/b-tech-in-computer-engineering-school-of-technology-pandit-deendayal-petroleum-university-gandhinagar-265363.

SNU-Noida is better than PDPU Gandhinagar according to placements and over all University rank.

JEE Mains college predictor is an online tool which predicts the probable colleges based on the difficulty level of the examination, average marks scored in JEE Mains and seats available in IITs, NITs, GFTIs, and other SFTIs. The rank predicted might not be accurate but it certainly does give an idea to the aspirant. Know your college admission chances based on your JEE Mains rank, home state, caste, gender, etc., here:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor