Write every time in the destination's local zone and label it, so nobody has to convert anything. Flight times are the usual culprit: a ticket shows departure in the origin's local time and arrival in the destination's, and people do the arithmetic wrong.
A "two-hour flight" that crosses three time zones isn't two hours. Someone reads the arrival time, mentally adjusts it, tells the group to meet at eight, and half the group is still in the air. It's not carelessness — the numbers on a ticket genuinely invite the error.
The safest version is nobody converting anything. bothways shows flight times in the correct airport-local time on a schedule the whole group reads the same way, so "lands at 6:45pm" means the same thing to everyone.