Hi, thanks for reaching out.
Yes, I think you can still have a shot if - IF - you are perfect in every other area. Your story, your ability to hit the right themes, your interviews (and having them work as a sales pitch that connects back to your apps), the whole thing. Your GMAT score is at pretty much the exact cutoff between "good luck, man, but you are probably screwed" and "eh, which it was higher." It is our belief that 660 represents that line. 660-690 is "wish it was higher" territory for most readers. Meaning: they won't just gloss over your file, let themselves off the hook, rationalize not reading it after a heavy lunch, etc. Under 660 and you both need a great story, but also a lot more applications because there's a good chance even the best story won't get read.
So your 660 is a blessing and a curse. It's a downside, but you just stayed above the danger zone. It does put a lot of pressure on your ability to execute the applications though. You have to really tap into the DNA of the schools, hit the key themes, showcase fit, showcase readiness (maturity + timing), all of it. I'm not trying to scare you off or, conversely, bully you into consulting (although you did pretty much fit the mold of the client we can help most), just lay it out for you.
As for schools, I think you can be fairly aggressive, but you want to avoid either small schools (they can't absorb as many lower numbers) or schools with monster average GMAT scores. So Yale, for instance, would be a bad bet. It's tiny and it has a huge avg GMAT. HBS and Stanford are going to super tough as well. I wouldn't rule any of them out because again, it is going to come down to everything else and I think you can get an adcom to wince and take that score if they love you enough. But those are three schools that will be particularly tough.
I would look at Columbia (rolling and you should submit before the scholarship deadline in early Jan) where your WE and professional potential might trump the score issue. Plus, the international focus is a good fit for you. Duke is a must for you to look at. Wharton is a longer shot, but it's big and is strong internationally. Stern. Booth. UCLA. Even Tepper. All worthy of consideration.
I hope this helps. We really can help you immensely, so feel free to PM me if you want to set up a free consultation.
Respectfully,
Paul Lanzillotti