Galicia
The Galician front was easily the most crucial for both Russia and AH in 1914, as it would determine whether or not the war would be won "before the leaves fell". Ivanov, the Southwest Front commander was quoted, perhaps apocryphally (ITTL), stating that the road to Berlin ran through Budapest. As it was, the Russians were to bring massive forces to bear on AH in August, with major reinforcements available from September onward. AH was viewed as the weaker enemy, despite their greater number of divisions on the Eastern Front, an opinion only enhanced by the maintenance of their 2nd army in Serbia.
In August the Russians were prepared to go on the offensive even if the AHs attacked them, but military intelligence, mainly determined by reports from Ruthenian AH civilians more loyal to their Slavic brothers, reported that AH forces were setting up on the defensive. Generals Ruszki and Brusilov, the commanders of the major attack force of the invasion, thought this was a ruse and relied on pre-war intelligence stating that the AHs were going to attack into the Ukraine. Ivanov only supported this perception and threw his forces into Galicia with the goal of achieving a decisive battle.
Despite German fears, it appeared the Russians were going to attack AH regardless of their passive stance, something that caused significant relief at OHL in Luxembourg once signals intercepts were passed on. AH intercepts also confirmed this, which caused Conrad to order that the San-Dniester line be 'prepared' by removing all civilians from the battle zone and clear fields of fire be prepared. Villages and forests were razed to the ground and trenches lines prepared for AH troops. Bridges were blown all over the areas of Galicia to be abandoned, AH administrators evacuated, horses and rolling stock were evacuated, and as many crops as possible purchased and removed from area of Russia advance. Disorder was left behind for the Russians as even gendarme and police forces were evacuated for use with the army.
Despite this seemingly favorable situation, AH military training had been geared solely toward offensive warfare, leaving many soldiers and officers unclear about the best way to conduct a defense and uncomfortable about their 'ignoble and unheroic' stance. It would degrade effectiveness once the battle was joined and reduced morale by abandoning so much land, including the 4th largest city in the empire and the administrative capital of Galicia, Lemberg. Indeed the declaring of the city as 'open' caused a fall in the Empire's prestige across the world and consternation both in the Empire and the Imperial court. Franz Josef was furious that he had to endure such humiliation*.
The Russian invasion commenced on August 26th, when the Russian 3rd and 8th armies invaded East Galicia, where they promptly overran Tarnopol and Brody. Further north the 4th army crossed the border around the same time, though the move through the Tarnew woods near the confluence of the San and Vistula delayed and disorganized the Russians. The 5th army took longer to mobilize and move out, which saw it only reach the AH border around August 30th, lagging significantly behind. All Russian forces had their goals, the 4th had Przemysl, the 5th Lemberg and then Sambor, the 3rd, Lemberg and the8 Styrj, and 8th Tarnopol and Stanislau, with further forces later to take secondary targets. When it was discovered that the AHs abandoned most of Galicia, movement forward became less cautious, as it was obvious where the AHs were waiting. Each captured major city was officially proclaimed part of the Russian Empire after a military ceremony, with the Czar arriving later to sanctify the annexation. All this further hurt AH credibility, but they were waiting for victory over Serbia before responding.
The wild advance had overextended the Russian forces, as rail heads were tens of miles behind the front and infrastructure had been sabotaged. A government had to be organized in the wake of the chaos left by the fleeing AH administrators. All this distracted from the goal: defeating the AHs and saving Serbia. But once the Russians actually did meet the AHs in battle, attempting to bounce their MLR, they simply bounced back. The defenses were too strong and the Russian advance had been confined between the Vistula and Dniester, right into the AH scheme. Though badly outnumbering their foe, artillery and munitions wagons lagged far behind the infantry and cavalry, preventing a breach of the trenches. Additionally food and other supplies were stretched beyond their limit, meaning that any advance was impossible even if the rivers could be crossed. Nevertheless the size of the Russian advance and the length of the front prompted Conrad to remove several units for the Balkans for use in Galicia.
In Central Poland the Kummer and Woyrsch groups were finding their reception less than enthusiastic, meaning their mission of raising revolts had failed. Now they had to contend with the Russian 9th army, as it advanced against them on August 26th. There was a bitter debate in the Russian command about whether it should head it East Prussia or Galicia, as it could tip the scales either way, with both the Northwest and Southwest Fronts demanding STAVKA give them the force. For the moment it would advance into Poland and be given orders to head north, south, or straight into Silesia later. September brought no more resolution to the debate, as the Russian 2nd army was defeated at Tannenberg and the Russian forces in Galicia stymied. The French wanted Silesia invaded and both Front commanders had valid points about its use. Paralyzed by the options for the moment it just pushed back the joint Austro-German force.
*This is the most unlikely part of this TL; Serbia could be left to wait, but the willful abandonment of Galicia is such a blow to the Empire diplomatically and politically that it is unlikely to be allowed by Franz Josef. He was an old school monarch, who was fixated on form and perception, rather than cold, hard realities. That was the Habsburg way, which even OTL played out in the organization of the war economy, a painful farce, which, thanks to Habsburg style, often hurt the conduct of the war. I am allowing it here simply to explore the option, but it is extremely unlikely. This is also partly the reason FJ told Conrad to attack even with insufficient force OTL, because a defensive stance would mean abandoning this major province. Because of this I consider my other ATL the most likely option rather than this.