Okay, so let's say Benedek steels himself and acts as decisive as he can at Königgrätz, winning the battle clearly, forcing the Prussians to retreat, which turns into a disaster as the Imperial light cavalry turns the retreat to a disorganized rout.
I suppose Saxony and the South German states remain in the Austrian sphere, and I suppose the sudden arrival of troops in Italy goes very badly for the Italians, going back to prewar status quo, with possible reparations from the Italians.
Can the Germans still unite the North German Federation? I know its a common trope for an Austrian victory to lead to Habsburg domination of Germany, but I personally think it would just cement the status quo, with no real solution. Would the bigger North German states lose faith in Prussia and be less inclined to support her in the future?
Would there be a war with France? I think not likely, at least not in the near future, which might work out well for the French, as their industry gains traction.
Would Prussia and Russia fall into a common camp? You guys seem to think so, but I think this is more complex: Prussia will have to choose between Britain and Russia, as with no German unification, there is no common German threat to those two, so the Great Game wouldn't wind down as it did OTL. So if Prussia allies with Russia, Britain will find her own continental allies. Austria would be a good candidate, and France as well, as there is little conflict of interest, and they have a common venture in Mexico (provided Britain doesn't recall her support and a victorious Austria helps out more).
Could this prompt Austrian reform? Now this is a complex question: Austria remains the nominal head of Germany, at least for now, but the Hungarian issue must still be solved. I am always an optimist, so I say that they may be more inclined to a federal solution, given that it's already "working" in Germany. Not too crazy of course, but right to the Hungarians, the Bohemians and Croats (maybe even the Poles and Italians?) could lead to a United States of Greater Austria/Danubian Federation, but that's way down the line. The thing is, if they give right to those three, they could have a free hand on oppressing and assimilating those less fortunate nationalities that were not given a seat at the table (Romanians and Slavs in Hungary, Serbs and Bosniaks in Croatia, etc), allowing Austria to also focus on her German sphere. This is extremely far-fetched, but a mind always races when thinking about a surviving Austrian Empire, in one form or another