Where would the Union's capital be if the south won the Civil War?

Realistically the chances of a Confederate victory were always dubious so I'm not sure if the Union had made concrete plans to move the Government. Lincoln noticeably refused to leave DC due to the potential effect on morale. I suppose Philadelphia might've been a potential capital but that's pure speculation on my part.

Still I'll try to give a brief overview of the Confederate capacity to attack the District. Initially, the Union expected a quick victory over the Confederates. When that failed, Lincoln moved pretty quickly to solidify control of the capital and the surrounding region. Union General McClellan was placed in command of fortifying an area that had not seen combat in over 50 years. He did pretty well and DC remained heavily fortified for the duration of the war. A direct Confederate assault was thus not seen as very feasible by Confederate leadership.

These fortifications may have led to Lee's focus on Maryland in the Fall of 1862. Lee hoped to take the battle to the American countryside in order to influence the upcoming congressional elections as well as to move the fight away from battle-weary Virginia. The campaign ended with Antietam and a confederate withdrawal.

Subsequently, while battles continued in the region between Richmond and DC there were few attempts to seriously take control of the capital. In the Gettysburg Campaign, you can see that the Union forces tried to stay between Baltimore/DC and Lee. The closest was the Battle of Ft Stevens in 1864 but the Confederates withdrew fearing high casualties despite limited union defenses.

Ultimately, Confederate attempts to seize the capital weren't very good and they knew it. Just like with them and Richmond (until near the end), the Union took special care to protect their capital. Either side capturing the other would've been a serious blow to their effort since both had major armies in the region that were responsible for protecting them (Potomac and Northern Virginia). In fact, this is how Grant ultimately secured a victory for the Union. Rather than focusing on Lee's Army, at the conclusion of the Overland Campaign, Grant snuck past them to capture an important supply city for Richmond. Lee, fearing an assault on the capital, retreated to Richmond. After a long siege, Petersburg (and Richmond) fell on April 2nd. This compounded with other problems plaguing the Confederacy (desertion, fewer men, heavily losses in other theaters, etc) was fatal. By April 9th, Lee had surrendered to Grant.