I need to fly from Eretz Yisroel to New York City after Sukkos. The most convenient day for me to travel is Motzoei Simchas Torah in Eretz Yisroel. The problem is that if I take this flight, I will arrive in America on Yom Tov Sheini. Is this permitted? And if it is, once I land, may I walk to the community where I will be staying, which is an hour away from the airport?
You may travel on Yom Tov Sheini as long as the airport is outside the techum Shabbos. However, you should not leave the airport. This is based on the ruling of the Shulchan Aruch (496:3) that if one lives in Eretz Yisroel and travels outside of Eretz Yisroel during Yom Tov Sheini, there is no prohibition to do melachah, as long as one does not enter a Jewish community.
My father, Rav Shlomo Zalman Auerbach zt”l, ruled that the airport has the status of a desert. Therefore, a resident of Eretz Yisroel is allowed to travel from Eretz Yisroel by plane to the airport on Yom Tov Sheini. Once there, that resident of Eretz Yisroel may do melachah while still in the airport. Since the airport is a place where people are arriving from all over the world, anyone there can assume that you came from Eretz Yisroel (as cited in Yom Tov Sheini Kehilchaso 3:27).
However, there are two reasons why it is forbidden for you to leave the airport. The first is that there is a problem of walking outside the techum. Furthermore, it is a zilzul to Yom Tov Sheini to walk outside the airport. Even if no one who is keeping Yom Tov Sheini knows that you flew in that day, it is still considered a zilzul to Yom Tov Sheini for yourself (see Yom Tov Sheini Kehilchaso 3:30 in the name of many poskim).
You do not need to be concerned that non-religious Jews will see you in the airport on Yom Tov Sheini and think that you have been traveling on Yom Tov. Most of them do not even know about Yom Tov Rishon, and there is therefore no maris ayin for them to see you doing something that is permitted.
Since you will be in the airport for 12 hours until the end of Yom Tov, I recommend that you bring some seforim to learn from. I highly recommend the sefer Yom Tov Sheini Kehilchaso, which has many p’sakim from my father and father-in-law.