If it were me, for three days I'd pass. I've always shipped my bike, never tried to schlep it through an airport, but I have dealt with large suitcases in airports before (smaller than a bike box), and I do schlep my bike to and from FedEx, and I can't ever imagine combining those two hassles.

Bring your running shoes, hiking boots, swimsuit - if you play soccer or basketball bring your shoes and troll the 'net for a pickup game ahead of time - whatever other cardio you do. That's my take.