Since I found out that most airlines don’t charge extra for bicycles in bags, I’ve taken my bike everywhere, from Tokyo to LA to Phoenix or Turin. Best way to discover a city, period.
However, most airports are far out and you need a cab or train to get into town. But Milan Linate is really close to the city, and yesterday I did the 20 minutes ride with my bike bag strapped to my normal bag:

Then packed it all up, right in front of the check-in area:

Then took a shot as it went through the X-ray machine (note the way the carbon fiber fork becomes transparent):

Then British Airways lost my bag.