Every year some news caster poses the question, “Could you get in a plane and fly all day to celebrate New Year’s continuously?” Theoretically you can. Here are three options.
Going the Commercial Route (and Taking Advantage of the Convergence of Lines of Longitude
Start at 57.8N, -175.5E (i.e., on the International Date Line) at 0000 1-Jan Local Time, flying towards Asia at 560 mph (at 560 mph, the cruise rate of a Boeing 777 at 31,000-35,000 feet). If you maintain this speed for 13 elapsed hours, you will maintain midnight local time continuously for 24 relative hours. However, there is one big caveat: you will need to find a way to re-fuel in-flight (as you will run out of fuel around 9 hours into the trip)
Going the Military Route (Doing it the Real Way)
Start at the equator at 180E longitude at 0000 1-Jan Local Time flying towards Africa at 1,036 miles at 60,000 feet (in an F-15 with conformal fuel tanks and three external fuel tanks). At this altitude you can do this without continuous firing of afterburners (you will be breaking the sound barrier, traveling at Mach 1.57). Re-fuel 8 times, using the afterburners to make up the loss of slowing down for mid-air refueling (you will need one extra re-fuel to make up for the lower efficiency of the afterburners). If you do this you will maintain midnight local time for both 24 elapse and relative hours (you will just need to use in-suit waste disposal system as you cannot get up to go the bathroom
I have no idea how much either of these would cost. Perhaps Richard Branson will offer it as an option soon.