You don't give us any details of the type of things you like to do, so that would help. Agree 100% with Salzburg, which is def. reachable for a weekend and would make a great place to spend one or two nights. If you get away early enough on Friday you can reach Salzburg (assuming no snow and using the Arlberg tunnel) in five hours, which would allow you to get in for a late dinner and then an evening wandering the streets of the Altstadt.
If you had a long weekend, Vienna is the obvious destination, but more of a flight than a drive. The stretch from Salzburg to Wien is long, straight and boring. That said, if you are wine lovers &/or foodies, the Wachau and the other wine regions around Vienna offer some of the best of those wine/food thingies in all of Europe.
If you are skiers / hikers, then Arlberg is a great place to spend a weekend and offers something for almost every budget (Montafon is pretty easy on the wallet, St. Anton a great mid-range place if you are into both ski and apres ski, and Lech/Zuers can break most people's monthly budgets over a champagne-filled weekend).
There's a lot more on the list: St. Johann in Tirol for family skiing, Kitzbuhel for a taste of the Munich "schikeria", Burgenland, Neusiedlersee, the Donau, etc. etc. Personally, I'd give Innsbruck a miss.
How many weekends do you have?