Phoenix Sky Harbor International Airport: This is the airport that matters. For Old Town/downtown Scottsdale, take a rideshare or taxi direct: roughly 20–30 minutes when traffic behaves, commonly about $30–45 (Uber’s cited average is about $37). A rental car is the better choice if you are staying outside Old Town or plan to hike, golf, or take day trips. Do not choose a shared shuttle merely to save a little: it can turn a short airport run into a multi-stop crawl. The free PHX Sky Train connects to the 44th Street station, but there is no rail into Scottsdale; continuing by bus is cheap but slow and awkward with luggage.
Phoenix-Mesa Gateway Airport: Useful mainly if your flight is much cheaper. Rent a car or use rideshare; expect about 45–60 minutes to Old Town Scottsdale and a substantially higher ride-hail fare than from PHX. There is no efficient public-transport transfer to Scottsdale.
Scottsdale Airport: A general-aviation/corporate airport, with scheduled JSX service noted in the local guide—not a practical commercial-airline alternative for most travelers. It is about 20 minutes by car from downtown Scottsdale; arrange pickup, rental car, or rideshare.