Let's enjoy the benefit of hindsight for the moment.

The choice was: to trade Willow for the box.

The effects were:

So looking solely at that, with the benefit of hindsight, did Buffy make the right choice? We might think yes, this outcome is acceptable. Casualties have been taken, but an immensely dangerous threat has been destroyed for only minimal loss.

But let's carry on anyway. Just for the heck of it.

Let's compare this with the probable outcome had the Box been destroyed:

Willow would remain the prisoner of the Mayor
It cannot be said whether or not Willow would have survived her imprisonment, perhaps she would not, perhaps the Mayor would kill her in a fit of rage about being defeated, but it follows the Mayor's character that he would have kept here alive (if not necessarily undamaged) to use against Buffy in the future.

à The Ascension would be halted
This is not definite but it is likely as Graduation gave every indication that the Box was crucial for the Mayor's transformation into the demon)

à The various casualties (both good and bad) of Graduation day would never have occurred

à Joyce would have been able to see her daughter graduate
Ahhhhhhh!

à The Mayor would have retained his position

Would he have retained his invulnerability? Once again we cannot know for sure, but evidence from the episode Bad Girls indicates that he would be invulnerable for the 100 days leading up to the Ascension, presumably once the hour of the Ascension had passed he would once again be pervious to harm.

What threat would he represent? With another hundred years to wait until the next Ascension the Mayor would be forced to go back to making deals with the underworld such as the one he made with Mr. Trick and using his 'committees' to intimidate any further undesirables that entered Sunnydale. But who are we kidding if we claim he wouldn't want to settle the score with a certain interfering Slayer and her pesky friends, especially if Faith is still knocking around and he has Willow locked up in a private cell (something which is surely not beyond his abilities). But if all he has are vampires, the only real threat he's going to represent is in making Buffy's life difficult in Sunnydale through more conventional measures

How could the threat he represented be marginalised or eliminated? A stake through the heart worked pretty well for Deputy Mayor Finch but the Mayor's always been very careful not to get involved in combat when not invulnerable (see Band Candy for a particularly rapid exit). Still if the hue and cry over Finch's death didn't produce enough evidence to pin on either Faith or Buffy even when the police were told that it could only be one of two people then its certainly a possibility that the Mayor could be 'marginalised' in a similar manner. They would be even more likely to get away with it if they used more mystical means that would be impossible for a mortal police force to trace. To be honest, the Mayor never really presented much of a physical threat until he became invulnerable. His power came from his influence rather than his body.

Ask again, did Buffy make the right choice?

Of course the actual situation was far more complicated. Despite Buffy's assertion that the trade was the only choice this is not strictly correct, at least five presented themselves, ranging from one extreme to the other

1. Complete the trade and wait until the Ascension
2. Complete the trade and plan to regain the Box before the Ascension
3. Attempt to trade but plan to double-cross the Mayor and retain the Box and regain Willow
4. Destroy the Box and attempt to rescue Willow
5. Destroy the Box and allow Willow to remain the Mayor's prisoner

Now add to this the similar options that the Mayor has open to him and you end up with a very complex decision.

Go to Masquerade's
Did the gang make the right choice in trading Willow for the Box?