Turned down Goldman Classics group for SA - Still FT possibility?

Ended up turning down GS SA offer for another top BB (MS/JPM) since I felt stronger about the group and, more importantly, they offered mobility to the NY office. After my SA stint this summer, would it be possible for me to recruit for GS or an EB in NY in case internal mobility at my current internship doesn't work out? And if so, what are the best steps for me to take now. When I do end up recruiting in the NY offices, should I mention that I had the offer or start afresh since it might look bad? And how often does this occur? Any information on this topic would be great - thanks!