Definitely in the center and place to be in Manhattan. Meatpacking district is right there, you can walk to the water / high line park and even Soho is only a few minutes away, you don't even need to get on a subway to get there.
The apartment is on the 4th floor, no elevator. If you're older or have heavy luggage (that you can't carry on your own), this could be an issue.
You can hear all the ACs in that one bedroom, which is towards in the inner yard. Besides that, the place was quiet, no street noise/sirens or anything. If you want the real NYC downtown experience, this place is right, plus you will have more space than in hotel rooms that are in the same price range.