Yes, you can usually drink tap water in NYC hotels. Most hotels in New York use the city's tap water supply, which is safe to drink.
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The water is safe to drink and meets EU standards for potable water. However, it may contain trace amounts of contaminants so if you're concerned about those, it's best to filter your own bottled water or use a pocket-sized portable filter when filling up from public fountains.
Europe's Water Is Generally SafeThe tap water throughout most of Europe is completely safe to drink. The taps in hotels, homes, restaurants and cafés all run with potable water. Of course, there's always room for common sense.