I love this question! 16 of my 22 vacations in Austria have been by car,. but also 11 days in Vienna. Austria is loaded with quaint villages and spectacular scenery, and, given the iffy EU weather, it makes it easy to adjust to good weather ( mountain scenery) or bad weather (villages, towns, museums). Drive to Salzburg to see the Wachau Valley, Krems, and Melk. The Abby Church at Melk is my pick for the top sight in Europe, but first go 6 miles beyond Melk on the N side of the Danube to see Maria Taferl Pilgrimage Church . Melk is Jakob Prandtauer's masterpiece. he warmed up by building Maria Taferl. If you see Maria Taferl first, you will leave the church thinking you have just seen the most beautiful building in the universe, and then Melk will make you forget it.
Skip Linz, but near Linz, don't miss Mathausen Lager, concentration death camp, (poorly marked road signs); St Florian Abby, Wilherring Abbey (Melk is the pinnacle of Baroque, Wilherring is the best of the Rococo)
Austria's best sights are concentrated in 1] an area defined by a clock face with Salzburg at 10:00; and west of Innsbruck.
Cute villages: Hallstatt; Admont; Bad Ausee {see Mahler's workshop & the 3 lakes); Bad Ischl; Hall in Tirol (near Innsbruck); Lienz & the Felbertauren road; Melk; Steyr; Zug; Krems; Admont, Radstadt; Lofer; St Johann am Tyrol; Ehrwald (great view of the Zugspitz); Zell am See: Solden and near Solden, Gurgl, Obergurgl (higher than Gurgl), & Hochgurgl (the highest Gurgl); the Salzkammergut towns.
Regarding Fussen: I assume you want to see Mad King Ludwig's castles. The road from Innsbruck is VERY slow going (unless they have improved it since 2009).
Regarding Hallstatt. Yeah, its a tourist trap, but it also a ** sight (below I will direct you to a nearby deserted **** sight). It is best by done by the approach from the south which I will describe later on.
Road trip to Hallstatt: Follow the river there the scenic Wachau Valley to Maria Taferl church, the second best work of the great Baroque archetect, Jakob Prandtaure. Then back track 6 miles to the Abbey at Melk, Prandtaure's masterpiece and in my book, the top sight in Europe. On to the Abbey Church just east of Linz where Bruckner is buried. Kids will be bummed out by the hundreds of skeletons stacked up in the church crypt. From Linz go north thru the Vlatavatal, (Moldau Velley) and lessen in classical music-- The Moldau is the second movement in Smetana's Ma Valast to Cesky Krumlov. Return to Linz. Go west along the river to the great Rococo church at Wilherring, then thru the Salzkammergut to Bad Ischl (Emperor's hunting lodge). Go up the mountain to Bad Ausee. Mahler did most of his composing in small shed (still there) on the shore of the first of three secnic lakes that run east of Bad Ausee. Continue south to the right turn for the road than runs along the north side of the mighty Dachstein. take the cable car up to the glacier and ice caves with great views of the Hallstattersee.
By approaching Hallstatt from the south, you can drive into town. The more common northern approach shunts you into a giant parking garage inside the mountain above the town.
From Hallstatt, go south to the base of the mighty Dachstein, turn right & right again to go north on the road parallel to the west side of the Hallstatersee, then left and left to the Gosausee. Once you see the Gosausee, you will forget about Hallstatt, a third rate scene in comparison. The Gosausee is the most spectacular Alpine lake in the universe, and nobody knows about it except the natives. There is a hotel on the shore and the lake view rooms are well worth the extra charge. The amazing scenic background for the Gosausee is the west side of the mighty Dachstein massif (the south side is the most scenic).