Pick a time and a city, and read it off in every other city. Daylight saving is handled for you.
Set the time in one city, and every other row shows the same moment there. The city you are converting from is marked and pinned to the top. When a city lands on a different calendar day, the row says so under the time.
Daylight saving is applied automatically. Because the conversion uses the real rules for each place, a time in July and the same clock time in January can differ by an hour between two cities, exactly as they do in life.
No currency of the calendar is fetched. The whole IANA timezone database, which is what every operating system uses, is shipped inside your browser. That is why this works offline and why nothing about your query leaves the page.
Add or remove cities freely. Build the short list you actually care about — a remote team, family abroad, a flight — and it stays put while you slide the time around.
You don't have to take our word for it. Every browser has a built-in panel that shows everything a page sends or receives over the internet. On a computer (this doesn't work on a phone):