The Arlberg lift pass covers Lech, St Anton, St Christoph, Zürs, Stuben and Warth-Schröcken. You can ski between Lech and St Anton in a day via the Flexen chairlift; the run is called the "Run of Fame" and takes you over 30km across the whole Arlberg massif if you do it end-to-end.
Lech's home area
The skiing immediately above Lech itself is mostly intermediate: long, wide blue and red runs off the Rüfikopf and Schlegelkopf chairs, plus a substantial network of beginner terrain at the foot of the Schlegelkopf and at Oberlech (5 minutes by underground funicular from Lech village; bizarrely brilliant). For families with younger children, Oberlech is genuinely outstanding: a slightly higher, sunnier, slower-paced satellite village with its own ski schools, gentle terrain, and proper restaurants.
Zürs
Five minutes by ski bus or fifteen minutes via the Madloch chair, Zürs is Lech's quieter sister. Slightly higher, slightly more snowsure, with the famous (or infamous) Madloch black run that takes you on a long, scenic descent back into Lech. We tend to ski Zürs in the morning and Lech in the afternoon to follow the sun.
Crossing to St Anton
If your family includes confident skiers, the trip across to St Anton is a proper adventure. The Flexen chair takes you up from Zürs, then a long run down into Stuben, then a series of lifts up to St Anton itself. Plan to spend the whole day, have lunch on the St Anton side (the Verwallstube at the top of the Galzig, perhaps), and ski back via the same route mid-afternoon.