As far as disruptions in the space-time continuum go, one day doesn't seem like much. Still, it's tough for me to wrap my mind around the International Date Line.
Phileas Fogg, hero of Jules Verne's "Around the World in 80 Days," famously wins his bet because he forgets about the date line. He circumnavigates traveling east, so from his perspective he gains a day. (He travels for 80 days and thinks he has returned to London on a Saturday. From the perspective of Londoners, it's only Friday. The denouement takes place the next day, when he realizes it's Saturday, not Sunday. Got it?)
We will be heading west our entire trip. That means that from our perspective, we will lose a day -- we will never go to sleep on the night of June 26 or awake on June 27. Instead, we will leave Honolulu June 26 at about noon. After an eight-hour flight that crosses the date line, we will arrive in Tokyo mid-afternoon on June 27.
Back home, 29 nights will pass. For us, it will be 28. (And no quibbling, please, about how it might be 30 days, counted another way.) As far as I can figure out, the only way we will ever regain that day is to take another trip some day, west to east.