Hi maggi10 - Thanks for posting, and apologies for the delays in responding!
Your GMAT is low but based on your other messages, it looks like you just took it again for a 680. That's in range for some good schools but it's also still difficult for a top school like NYU based on how competitive your candidate pool is.
You're quite young already and a younger profile needs to be a little more impressive in order for the schools to say 'yes', particularly at NYU or Kellogg. Many schools could take a pass if there are any pronounced weaknesses, only because they know that you have time to work to fix them and you could then try again next year. So the bar is a little higher for younger candidates.
The TOEFL is typically recommended as the best English test to take because it's universally accepted.
We cannot suggest schools without knowing a lot more about you - sorry! We explain why in this other thread
There's a lot of other queries from candidates like you on these boards, you may want to keep reading and see what you can learn from them.
If you're trying for Round 1 then you're getting started a little late!! Hopefully you've already made good progress on your essays. The essays will matter ***a lot*** and they take more time than most people expect.
You might want to check out The Indian's Guide to Getting In
which is a special book we've written just for candidates like you.
Good luck with your applications and please stay in touch!
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