What kept Angmar out of Bree and the Shire?

[BalrogRingDestroyer]

It seems that they got Fornost (or it's abandoned anyway), they got Amon Sul (what's now Weathertop) and they got some area that's now the Barrow Downs. The Barrow Downs area was the most western area that they got into that I can think of. However, it seems that something kept them out of Breeland and the Shire. Come to think of it, the Tolkien maps show an area in the north saying "Here was Angmar of old" or something like that, so it seems that Angmar is no longer around by the time of the Fellowship of the Ring. Did it fall from some last ditch efforts of Arnor or did it fall when the Witch King disappeared after Sauron lost the Ring at the end of the Second Age?

Actually, whatever happened, it seems that the Breeland and the Shire avoided most of the stuff with the War of the Ring, save some visits from the Nazgul, until after the fall of the Dark Tower when Sharky and his ruffians caused a bunch of trouble in both. (Well, maybe Bullroarer Took got involved at some point with a goblin invasion, too, now that I think of it, though I'm not sure if Sharky or Golfimbol caused more damage to the Shire.)

 

[Tom Bombadil is not god]

I think that the old forest is on the border of the shire witch should keep people out along with the brandywine river.

 

[Ent]

though I'm not sure if Sharky or Golfimbol caused more damage to the Shire.

Definitely Sharkey. Bullroarer stopped the invasion. Sharkey took over the whole of it until the Saviors came back.
There are answers to the primary question but I need to look a few things up so I don’t mislead. Will be back to this absent someone else getting to it before I’m able to get it done.

 

[Olorgando]

... so it seems that Angmar is no longer around by the time of the Fellowship of the Ring. Did it fall from some last ditch efforts of Arnor or did it fall when the Witch King disappeared after Sauron lost the Ring at the end of the Second Age?

The Second Age had nothing to do with the Witch-king of Angmar. As per Appendix B "The Tale of Years" for the Third Age, he first goes to Angmar around the year 1300 TA (about this time the first Hobbits settle at Bree). He first invades Arnor in the year 1409 TA. The first Hobbits settle in what was to become the Shire in 1601 TA. The end of the North kingdom - its remnant Arthedain - occurs in 1974 TA. But the Witch-king's forces are annihilated by an expedition from Gondor in 1975 TA, just as Sauron's forces in Eriador were annihilated in 1700/1701 Second Age by an expedition from Númenor, and the W-k disappears from the north. Bree and the Shire were too far south from the W-k's main, or sole objective, Arthedain; and probably, if he knew about them, considered irrelevant in his war aims.