I would say protesting at a port would be less likely to garner international attention, and probably would be easier to shutdown quickly and relatively quietly.
Shutting down an airport is much more public, therefore probably safer in the long run. Also more likely to be reported on because it affects the public in a more direct way. Yes, it inconveniences some people, but it gets the message out.
Either way, I doubt it will do much to change anything soon enough.
Independence Day (1996)
They just walked in to the underground lab beneath Area 51. The president was curious how it was paid for.