In Hobart, the airport security guard offered to dispose of them for us!!!
In Portsmouth, our BnB host wasn't too bike friendly. So after building the bikes, we cut the cardboard into smaller pieces, strapped them on the back and randomly deposited them into dumpsters and trash cans over the next hour.
In Oslo, we left them with our friends hosting us...I'm sure their kids loved to play with them.
In Denver, I left it in the luggage security area (@ $10/day) because It was only a few days and DIA is way out there. Storing the box was cheaper than a taxi back out to the airport.
That's all I can recall,
Enjoy the trip,