Time zone tools are small things that remove a surprising amount of daily friction. A world clock widget on your phone showing home and your new city ends the constant mental arithmetic, and once family cities are pinned there, you stop accidentally calling your parents at dawn. Most phone clock apps do this natively; no special downloads needed.
For work, the real lifesavers are calendar features. Setting your calendar to the new zone immediately, enabling dual time zone display, and using meeting schedulers that show every participant's local hour prevent the classic newcomer blunder of proposing a meeting that lands at midnight for half the attendees. When emailing across zones, scheduled-send features let you write at your convenient hour and deliver at theirs, which reads as considerate and keeps replies fast.