re: Is NYC really worth the incredibly high prices?

You can do it for a lot cheaper than that fwiw. Pretty accurate (if not underestimating) for the food costs, but that's honestly everywhere now. I stayed at the Hyatt Grand Central for under $150/night last march- connected to Grand Central and there's a shuttle train that will take you to Times Square. Very easy to navigate from there and the area is fine. Hotel is just slightly outdated, but it's really not that bad.