Hi! It is very hard to say you have a good chance or no chance at a top tier school without knowing more about your and your experiences - at work, in school and through your outside activities. That being said, a 680 GMAT score is on the lower end of the range for many of the top 15 schools. If you had the time, you could take the GMAT again to see if you could bolster your score.
As for your recommendations, I always advise my clients to ask people who know them best. Many schools require you to ask a direct supervisor, because they can most accurately talk about you and your experiences. In order to make sure your recommendations are full of detail, I often suggest giving your recommenders some guidance on your top accomplishments. That way they can draw from that when writing up your recommendations.
Best of luck,
Rachel Beck
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