NYU has good support for their postbaccs but it's not very cost effective - I would recommend CCNY or Hunter as it would be cheaper and also more feasible to take the upper division science courses as well as the prereqs without paying an arm and a leg.
For NYU, summer session tuition will run about $10,000 for Gen Chem 1 and 2.
Around 21,000 for fall and spring semester = $42,000.
$10,000 + $42,000 is about $ 52,000.
For 1 year full housing near NYU, expect to pay at minimum $1500 a month (unless you get a nice share with a roommate).
Cost of living would be about $1000 a month (plus or minus depending).
That would bring the grand total up to $82,000 for one year if you live near NYU. This number does take into account extra school fees such as textbooks, which if you don't buy wisely will easily total another $1000.
Unless you have the money, NYU isn't worth it. All of the lecture classes are HUGE (bio with about 500 students) and it will be a bit harder to get recommendations with professors unless you visit them every single week. The advising at NYU is decent and the program itself is fine, but I wouldn't recommend it compared to other much cheaper schools.
Remember that unless you can pay out of pocket, this $82,000 will accumulate interest for at least 6 years before you begin paying it off if you continue on to medical school (which with loans might run up another $300,000). If you have any previous debt this will be even larger. For med school it might be inevitable you will have to take on a lot of debt, but it's not necessary to take on so much right now. You can find programs of at least the same or higher quality for much less money.
While I don't think finances should be the main influence in your decision about being a doctor you don't want to be 50 still paying off school loans with a mortgage, car loans, etc. If you can avoid the extra costs, by all means avoid them!