Stayed in Stuben 2009 and regularly visit St Anton, so know the area reasonably well.
The skiing around Stuben is really nice, if a little limited. It’s always quiet which is the appeal of the place for me. The off piste is supposed to be amazing but not done (yet). Don’t think you really need the car to be honest. You can get into the St Anton circuit from Stuben on ski and can ski all the way back (7km run). To get to Lech and Zurs you can either get the Post bus from Stuben or ski to Alp Rauz (Valfragerbahn) and get the free and regular bus (one way takes you to St Anton via St Christoph and the other way takes you to Zurs then Lech). If you have the car I’m sure you’ll need to pay in St Anton and Lech to park - might be free in Zurs.
Where are you staying? We stayed at the Hubertushof and loved it. The Mondschein serves michelin star food and the Berghaus Stuben used to be an excellent lunch stop but now has new owners and is nowhere near as good. The original owners now own the Haus Schneider on the mian st, so probably worth walking to for lunch - although I only discovered this after we came back from St Anton this year.
Not much happening at night but the Hotel Post is usually quite good as is Willy Pils’ Stuberl for some apres drinks.
Enjoy Stuben before they upgrade all the lifts next year - as I suspect this will increase the traffic.