One resort for the whole trip, or split it?
Because all three sit within roughly an hour of Innsbruck Airport and of each other, a multi-resort trip is genuinely realistic here in a way it isn't in most ski regions. Whether it's worth doing depends on trip length.
A long weekend (3–4 days): pick one
With this little time, the drive/transfer time of splitting resorts eats too large a share of the trip. Pick based on the comparison table on the homepage and commit — Kitzbühel's 188km and Innsbruck's nine-area spread both comfortably fill 3–4 days without repeating terrain.
A full week (6–7 days): still probably one base
St. Anton's 302km plus off-piste, or Innsbruck's nine linked areas, both have enough genuine variety to fill a full week from a single base without a transfer day. Kitzbühel's smaller 188km area is the one most likely to feel repetitive by day five or six of a single-base week.
Ten days or more: a two-base split starts to make sense
A realistic split is Innsbruck for the first half (city logistics, easy arrival, varied terrain) and St. Anton for the second (committing to the bigger, more serious terrain once you're acclimatized), connected by the roughly hour-long transfer described on the getting-there page. Kitzbühel pairs naturally as a shorter add-on at either end given its own similar distance from Innsbruck.