[Galadriel55]

Sauron wouldn't be any more after Bree than after any other settlement not yet under his rule, I don't think. It has strategic importance as a "crossroads" town, but no inherent value beyond that. Sauron doesn't particularly care about occupying Bree in LOTR as it would come in its turn, after the stronger forces of Gondor, Rohan, Dale/Erebor, etc are subdued and he has free access to the poorly defended west.

However, it wasn't so much Sauron as Saruman who was after that corner of Middle-earth. Saruman had men stationed there, probably gathering all the news coming in from all four roads and passing them along via the likes of Bill Ferny and his southern friend. Was Saruman after Bree? Not really, but he made full use of it strategically, and he was after the full use it could give himm. He was going after the Shire, in a desire to exploit and later to simply spoil out of spite (was it the same with Fangorn Forest?). But his later and more devastating shenanigans in the Shire were driven by personal motive, not military or political plans.