The Habsburgs, who ruled Austria-Hungary and a bunch of other territories, indirectly ruled Germany as emperors until Napoleon came along like the combobreaker he was and dissolved the Holy Roman Empire. The German states had never been theirs, but half of Europe had been or was, so apart from already sort of ruling Germany, they had a lot of territorial claims to press. Some of those were hotly contested and required the investment of a lot of political and military capital.

Territorial expansion of the Habsburg/Austrian/Austro-Hungarian Empire was mostly focused on Italy and the Balkans, less controversial targets for campaigning. They held power in Germany, but never enough to unify it politically. The German states were fiercely independent and probably would have been supported by much of Europe to resist invasion. The Empire was already really big and had tentacles all over Europe by having ruled much of it at one time or another, so fear of Habsburg encroachment on national sovereignty was widespread.

After Napoleon, the Prussian state had grown so big it would eventually take over Germany and the Austro-Hungarians were probably sick of war after getting spanked by Napoleon several times. They had needed Prussian help to win (and also to lose a couple of times), a prelude to the BFF status between Germany and Austria that would later develop. It's always very hard to really determine motivations, since politicians generally lie about them, so this is just a couple of things I would expect to have played a role in the decision to not invade Germany.

Edit: Also, finally, the German states weren't city states, they were mostly somewhat smaller kingdoms, so it wasn't like the Austrians could levy completely overwhelming numbers.