If you are going to the Zell am See/Ski Circus area, be aware that the same lift pass covers Zell am See, Kaprun, Kitzsteinhorn, Saalbach, Hinterglemm, Viehhofen, Leogang and Fieberbrunn. My recommendations in terms of which villages to stay in are:
Best choise - Saalbach-Hinterglemm. Lots of affordable hotels, apartments and cosy B&Bs (called "Pension" in Austria) clustered around the centres of the villages and close to the lifts. Most are within a 5-10 minute walk of the nearest lift - the more expensive hotels are ski-in/ski-out. Saalbach-Hinterglemm probably has the largest snow-making capacity of anywhere in the Alps, and certainly has the fastest and most modern lift system.
Next best - Zell am See. Zell is a larger, busier town and of course it has the stuning location next to the lake. The downside is that the hotels are further away from the lifts, so you either walk through the town to the City Xpress lift, or take a crowded ski bus to the Schmitten area. Neither option is great with two children in tow.
Finally - Kaprun. There is a small skiing area at Maiskogel, but the advantage of Kaprun is access (by car/bus or using a series of cable cars) to the Kitzsteinhorn glacier. Personally this would only be the back-up option in the unlikely event that there is too little snow in Saalbach-Hinterglemm or Zell am See.
Other options I'd consider (I'd actually choose either of thse in preference to Kaprun if there is sufficient snow):
Viehhofen - a very small village just outside Saalbach which has a lift that goes up to the Schmittenhohe in Zell am See, and a 5-minute bus connection to the Schonleitenbahn lift which is the entry point to the Saalbach-Hinterglemm area. There is some excellent affordable accommodation there, and although the village has very little night life, I'm assuming that this is not a priority for a family with small children.
Leogang - another small village, but be aware that the lifts are outside of the village centre at Steinberg and Asitz, where there has been a huge amount of building activity in the last 5 years and where there are now some very stylish apartments and Apartment Hotels next to the base stations of these lifts. Leogang is on the "cold" side of the Ski Circus - i.e. the slopes are mostly in the shade - so when snow cover is less good elsewhere, Leogang always seems to have excellent conditions. It also has some of the best mountain restaurants in the area - three at the top of the Asitz/Steinberg lifts (these lifts meet at the top) and one at the mid-station of the Asitz lift.