Also, I'm not sure about the subway system. If they have a sign saying "no guns", they will have a problem with someone carrying a katana onboard.

Quite a few years ago my sensei and I were heading for a major Iaido seminar in Manhattan. Top floor gyms at a large downtown high school. Nakanishi Sensei 9th Dan, was guesting (forgive my spelling)
We were both stopped by a police officer in the subway leaving the bus depot. Our blades were in cases. A quick explanation where we were heading sufficed. That was WAY before 9/11.