My future supervisor invited me for a two-day visit, flew me from New York City and got me two nights at a nice hotel. On campus, I gave a seminar in front of a somewhat large audience. I got to talk to some graduate students, some professor working in related fields, and some post-docs. A really pleasant experience overall. I was aware that I was the only candidate matching the profile, because the job had not been filled for two years and my future advisor told me so. He also knew that I had other options, so he had to work to convice me to come.