Sorry to hear you're having an issue, and i'm surprised you're having such a tough time, as things like this are usually resolved fairly quickly once you can get somebody on the line that understands the issue (it's this second part that can be difficult). I think this could easily be resolved without the need to send a certified letter... in the future feel free to post here first as we have a pretty good understanding of how to navigate these type of issues.
Through a little research it's clear that they have inadvertently plotted this hotel at the same exact location at the Hyatt Place New York Midtown South, which is indeed in the Empire Stat Building zone. If you click this previous link and scroll all the way to the bottom of the page you can see the location for the Hyatt Place Midtown South is at the same exact location that they have placed the HYATT PLACE TIMES SQURE... this is usually enough to get them to stop reading from the script and reach out to a manager (or you can ask to speak to one). As well, at the 2nd link it is clear that they have placed the hotel on 36th St, even though the address above indicates that the Hyatt Place Times Square is on 39th St (further evidence that the location they are looking at is not correct).
You can wait for a responce from your certified letter, but if you can get this escalated to the 'next level' of PRICELINE customer service, i'm sure it will be resolved very quickly using the technique above of:
1) they have put the hotel at the same location as another Hyatt Place property
2) the address of the hotel is on 39th St and their plot is clearly not 39th St
3) if they use another source to look at the address of the hotel (google, Hyatt website, etc) they will see it's in the Times Square zone
Of course i'm in agreement that you shouldn't need to do any of this, and the hotel should be zoned correctly to begin with, but it looks like an honest mistake that hopefully will be fixed shortly.
Please remember to return to BetterBidding and use the PRICELINE and HOTWIRE links on the board to begin your travel purchases... or thru our sister site MAPSandHOTELS.com for your regular rate purchases.
Let us know how you ultimately make out.