Hey theDr,
I had the same GPA and 22/23/17 on my DAT. I was accepted to all the schools I applied to except for havard (Didn't even send me a rejection letter, wasn't even worth a stamp I guess). I studied for the DAT for a month and a half (took kaplan) and took the DAT in the middle of july. My recomendation is to apply as early as possible so that you can make it into the first application cycle. I sent in my ADSAAS application in the middle of augast and had my pre-med advisor send my transcript and LOR's directly to the schools.
For Columbia try to crack a 20 AA, they are a big DAT school as you may already know. As for NYU, well with your GPA and 18 is more the enough. Good Luck