You may write SAT for Universities Abroad, but I will advise you against it. It is always preferred to complete your Bachelors in India, focussed on Research followed by Masters/Doctoral Education Abroad for better Career Scope and Prospects besides being able to get a Good Deal of Funding for Graduate Admission Abroad.

Among your options, I believe your preference should be Manipal followed by AMITY. Both are leading private Universities with excellent infrastructure and faculty, however the project training and research culture and Institute Reputation is much higher for Manipal University, and may greatly benefit you during Graduate Admission and Application Procedure.