It doesn't matter how much you'd saved for your vacation. If you're going to spend $600 a night in a New York hotel, then your money won't last that long. I'm sure NYC is definitely not the most expensive city to visit in the world so supposing one want to save money when they're traveling, which cities should they avoid?
I have compiled a list of some of the most expensive cities: Singapore Melbourne Paris Oslo Tokyo Geneva Sydney
Your vacation is going to be as expensive as you want it to be. There are obviously cheap hostels you could stay with in NYC. I would say in general western Europe, Japan, and the US are pricey destinations. If you really want cheap travel, you'll have to hit up africa or southeast asia -- which I highly, highly recommend! The best trip I ever took was to Vietnam and Cambodia.
Japna is definitely expensive destination for travel in Asia. Otherwise, South-East Asia has the best destinations for chill yet adventurous budget travel