Sorry about my delay in replying--somehow missed your post until now.
It's tough to hear bad news, so my heart goes out to you for working on so many applications without a fruitful result. Very difficult to ascertain why you were rejected, but a couple of things jump out. You said you applied to Fuqua without an interview, and since Fuqua allows everyone to interview, that would definitely have contributed to your rejection there. They don't let anyone in whom they don't interview. I would definitely recommend a reapplication there with an interview this time (go round 1). Curious if you were able to get any feedback from any of your target schools on your rejection.
As for your specific questions:
Should I take the GMAT again? Not necessarily. If you thought you could boost your score by another 30 points or so it might be good for reapplicant status since it would demonstrate an improvement over this past season's apps, but in general, having a 700+ on your application is what you need. Your applicant pool is simply so darned competitive that it becomes increasingly difficult to stand out. Without a full review of your past applications, it would be tough to point to specific reasons, although my guess is it comes down to this whole not standing out thing. Perhaps your story lacked conviciton or something memorable and unusual. Most Indian applicants worked in the Tech field and volunteered with NGOs and organized festivals and played Cricket, etc. so it just tough to seem different.
Should I re-assess my goals?
This likely was indeed a contributor to your demise last year, since I don't see the clear connection between what you have done and an investment banking or VC career. Without some really convincing evidence that you would be attractive to these industries, the schools likely viewed you as a risk of not landing a job within the critical 3 months after graduation and potenially hurting their precious rankings stats. You may want to revisit your goals and see if you can cast a vision more in line with a natural career progression (example: financial services consulting??) Schools tend to like to see intentional choices and forward career momentum and not as much the pie in the sky, let's use b-school to reboot my career and get a sexy job approach.
Should I improve the essays (presentation, content etc.) without changing the goals?
I think revisiting the goals is important in your case and while I am not at liberty to do a full reading of your applications from last year on this forum, I can also guess that improving the essays along with the goals would be a good combo
Should I target some other set of schools? Please suggest a few. I am currently thinking of Kellogg, UCLA Anderson, Yale, Tuck, INSEAD. But if I think the school selection was not a problem, the problem was somewhere else.
For one thing, there were really no safety schools in your mix. Always good to pick a range of schools when applying. All your choices seem to be top 10 type schools, so I would say don't be afraid to look beyond that--if you stay in the top 25 you will likely get all you need education wise and also access to the types of emloyers (consulting and banking, etc.) that you desire. Even if you cast your vision around something other than ibanking, you can still go for those jobs once you are in school. There are plenty of regional banking jobs that can be just as rewarding as the buldge bracket banks in New York. possibly even a more rewarding lifestyle as well.
If I were you, I'd assess this year critically and decide if I had enough interesting or progressive changes or advances in my career to warrant a reapplication. Besides Fuqua, who could have simply dinged you because of the interview thing, schools are going to be looking for improvements since your last application in your profile. If you don't feel you have anything new to offer, I would indeed select a new slate of schools, perhaps broadening my target a bit more, and working with someone (a consultant or at least someone who has been to b-school) on your story packaging and overall presentation. No reason why someone with your profile should get dinged by every school. Who knows? maybe you just had some careless mistakes in your applications. B-schools hate that! Hope this helps.