The text does not make it quite clear, so it is difficult to determine where they really went to after they had left the battlefield. We do know, however, that King Duncan had instructed Macduff to call on him in the early hours of the morning, for he says:
He did command me to call timely on him:
I have almost slipp'd the hour.
Macduff is saying he was almost too late for his appointment with the king. In his report about where they had spent the night, he mentions the following:
The night has been unruly: where we lay,
Our chimneys were blown down; and, as they say,
Lamentings heard i' the air; strange screams of death,
And prophesying with accents terrible
Of dire combustion and confused events
New hatch'd to the woeful time: the obscure bird
Clamour'd the livelong night: some say, the earth
Was feverous and did shake.
Macduff's speech does not make it entirely clear where they had spent the night but he does indeed convey that it was an unnatural time. There had been terrible gales which were so powerful as to destroy chimneys. They had heard strange noises, loud predictions about a coming doom and strange cries of death. They heard reports of fires burning and new calamities about to arise and create an atmosphere of sorrow. The owl hooted throughout the night and there were reports of an earthquake.
These events clearly indicate that nature has come into rebellion. Such unruly acts in nature usually, as was believed in Shakespeare's time, foreshadowed some terrible event. In this instance, they are soon to learn about Duncan's murder.
Both Lennox and Macbeth agree that it had been a terrible night.
We can assume that Macduff and Lennox may have been instructed by King Duncan to tie up any loose ends after their victory over their enemies. The two did not accompany Ross to the arrest and execution of the traitorous thane of Cawdor, whose title had been bestowed on Macbeth, so they must have gone to complete some other official tasks. They probably spent the night in a village close to Macbeth's castle, where they heard all these terrible sounds and predictions, before heading to Inverness.