I live on the East Coast, and before my AN was diagnosed, I served on the board of wonderful organization on the West Coast and made regular trips. I wondered why after almost every trip I awoke with vertigo and had to sleep it off for several hours before I could function again. The vertigo eventually morphed into daily dizziness, and the thought of getting on a plane was too horrible, so I gave up my board position. Now, several months later, I just took a plane trip to the Rockies and had no attacks. I think the balance nerve on the non-AN side is coping well, and I am delighted to back in the air.
I wanted to chime in because I think that for those who do have serious vertigo or dizziness, plane trips may exacerbate the problem (in my non-medical, humble experience). If you are not experiencing serious vertigo/dizziness issues now, I don't think a plane flight would be a problem. As a precaution, you'll want to stay well hydrated.
Have a great trip!