A world clock displays local time in several cities, but each display should refer to the same underlying instant. The date may differ across cities even when the clocks update together.
Add cities with named IANA zones and compare their current offsets. Check a future date separately if you are scheduling: daylight-saving rules can change the offset between now and the event. A static abbreviation or a present-day offset is not enough for a future invitation.
For important coordination, share a calendar event or UTC instant as the common reference, then let each participant view their local time.