What happened to the Rangers of the North after the War of the Ring?

Question

In The Return of the King, Halbarad and at least two dozen other Rangers of the North come to Aragorn's aid. Halbarad, and possibly some others, die in the Battle of the Pelennor Fields, and it is possible that more may have died in the Battle of the Morannon.

Later, when Gandalf and the hobbits return to Bree, Butterbur the Innkeeper laments the departure of the Rangers, which had led to a significant deterioration in living conditions throughout the region. Gamdalf comforts Butterbur by saying that the Rangers have returned to the area, riding with himself and the hobbits.

But the hobbits are the only people riding with Gandalf, so it appears that Gandalf is referring to the hobbits.

All of this led me to wonder what happened to the Rangers after the war, where they went, and if they had returned to the north before Gandalf and company, why they didn't do anything about Sharkey and his goons.

---

Note: Here is the conversation in question. Just before this, Butterbur mentions how dangerous the roads have become; the hobbits say they have encountered no problems approaching Bree; Butterbur says their swords and armor would have scared off the ruffians, and Gandalf says the Inn, too, will be safe as long as he and the hobbits are there.

'How long will that be?' said Butterbur. 'I'll not deny we should be glad to have you about for a bit. You see, we're not used to such troubles; and the Rangers have all gone away, folk tell me. I don't think we've rightly understood till now what they did for us. For there's been worse than robbers about. Wolves were howling round the fences last winter. And there's dark shapes in the woods, dreadful things that it makes the blood run cold to think of. It's been very disturbing, if you understand me.'

'I expect it has,' said Gandalf. 'Nearly all lands have been disturbed these days, very disturbed. But cheer up, Barliman! You have been on the edge of very great troubles, and I am only glad to hear that you have not been deeper in. But better times are coming. Maybe, better than any you remember. The Rangers have returned. We came back with them. And there is a king again, Barliman. He will soon be turning his mind this way.

'Then the Greenway will be opened again, and his messengers will come north, and there will be comings and goings, and the evil things will be driven out of the waste-lands. Indeed the waste in time will be waste no longer, and there will be people and fields where once there was wilderness.'

Mr. Butterbur shook his head. 'If there's a few decent respectable folk on the roads, that won't do no harm,' he said. 'But we don't want no more rabble and ruffians. And we don't want no outsiders at Bree, nor near Bree at all. We want to be let alone. I don't want a whole crowd o' strangers camping here and settling there and tearing up the wild country.'

'You will be let alone, Barliman,' said Gandalf. 'There is room enough for realms between Isen and Greyflood, or along the shore lands south of the Brandywine, without any one living within many days' ride of Bree. And many folk used to dwell away north, a hundred miles or more from here, at the far end of the Greenway: on the North Downs or by Lake Evendim.'
-The Lord of the Rings, The Return of the King, Book VI, Chapter 7: "Homeward Bound"

Answer 1

Short answer: we don't know. We do know from appendix A that Aragorn restores the city of Annuminas after the war:

... when he [Aragorn] comes north to his house in Annuminas restored and stays for a while by Lake Evendim, then everyone in the Shire is glad.

In Homeward Bound, Gandalf hints that Aragorn also intends to restore Fornost.

And the King will come there one day; and then you'll have some fine folk riding through.

Now some Dunedain must already have been living at least partially settled lives; maintaining the blood line for sixteen generations would require a safe place for children to grow up. The Chieftains of the Dunedain were fostered in Rivendell, but there is no evidence to suggest that other rangers grew up there. Moreover, in the Tale of Aragorn and Arwen (Appendix A), Aragorn's mother Gilraen leaves Rivendell and returns

to her own people in Eriador.

In conclusion it's likely that the Dunedain returned to their ancestral homes when these were restored. For any that didn't fancy city life, there were still the orcs of the Misty Mountains to deal with, plus wolves, trolls and probably assorted other nasties that we know nothing about.

Answer 2

It's implied that they settle down, building some permanent settlements, and have trade & communication with Gondor. See e.g. Gandalf's conversation with Butterbur on the return trip.