TL;DR: The opening chapters of Treasure Island make it clear that the "Admiral Benbow" must be within a few miles of Lynmouth in Devon.
Stevenson wrote a detailed account of the writing of Treasure Island. Although this does not mention the "Admiral Benbow" or its location, it does include the passage:
… how troublesome the moon is! I have come to grief over the moon in Prince Otto,* and so soon as that was pointed out to me, adopted a precaution which I recommend to other men—I never write now without an almanack. With an almanack, and the map of the country, and the plan of every house, either actually plotted on paper or already and immediately apprehended in the mind, a man may hope to avoid some of the grossest possible blunders. With the map before him, he will scarce allow the sun to set in the east, as it does in The Antiquary. With the almanack at hand, he will scarce allow two horsemen, journeying on the most urgent affair, to employ six days, from three of the Monday morning till late in the Saturday night, upon a journey of, say, ninety or a hundred miles, and before the week is out, and still on the same nags, to cover fifty in one day, as may be read at length in the inimitable novel of Rob Roy.
Although Prince Otto (1885) postdates Treasure Island (1883), nonetheless the passage shows that (unlike Sir Walter Scott) Stevenson cared about geographic accuracy and detail, and so he may have had in mind a specific location for the "Admiral Benbow", and we might be able to deduce it if we pay close attention to the text.
The "Admiral Benbow" is somewhere on the coast of England where the topography consists of small coves backed with cliffs. Chapter 1:
When it [the rum] was brought to him [Billy Bones], he drank slowly, like a connoisseur, lingering on the taste, and still looking about him at the cliffs and up at our signboard. "This is a handy cove," says he, at length; "and a pleasant sittyated grog-shop. Much company, mate?"
Chapter 4:
The hamlet lay not many hundred yards away, though out of view, on the other side of the next cove
In the winter, sunlight can be seen reflecting from the sea before it shines into the cove, hence the cove faces west, north-west, or north. Chapter 2:
It was one January morning, very early—a pinching, frosty morning—the cove all gray with hoar-frost, the ripple lapping softly on the stones, the sun still low, and only touching the hill-tops and shining far to seaward.
A coast road to Bristol passes the inn. Chapter 1:
When a seaman put up at the "Admiral Benbow" (as now and then some did, making by the coast road for Bristol)
To reach Bristol requires an overnight journey by stage-coach. Chapter 7:
Next moment we had turned the corner, and my home was out of sight.
The mail picked us up about dusk at the "Royal George" on the heath. I was wedged in between Redruth and a stout old gentleman, and in spite of the swift motion and the cold night air, I must have dozed a great deal from the very first, and then slept like a log up hill and down dale, through stage after stage; for when I was awakened at last, it was by a punch in the ribs, and I opened my eyes to find that we were standing still before a large building in a city street, and that the day had already broken a long time.
"Where are we?" I asked.
"Bristol," said Tom. "Get down."
How long would this journey have been? Wikipedia says:
The stagecoach traveled at an average speed of about five miles per hour, with the total daily mileage covered being around 60 or 70 miles.
A look at a map of southwest England shows that the only places meeting all the requirements are in north Devon. Lynmouth fits the bill perfectly: it has a north-facing cove, cliffs, a coast road, and it's 75 miles from Bristol. Too far east of Lynmouth and you lose the cliffs; too far west and you lose the coast road and can't reach Bristol overnight.
Charles Stephen Brooks agrees with my analysis in English Spring (1930):
Countisbury Headland juts into the Channel just up the coast from Lynmouth. Its huge curve might be the back of some great creature escaped from chaos. It is a long climb and it is steep. The road is cut against the headlands and has an unobstructed view. Lundy's Isle, far out at sea, marks the entrance of the Channel. A northern smudge of land is Wales. There is smoke of frequent ships. If one follows the Countisbury Hill a few miles farther towards Porlock and peers down into each hollow of the rocky shore many hundred feet below, he will presently see the very scar and beach where Stevenson placed the Admiral Benbow Inn of his Treasure Island—the very path on which Blind Pew came tapping in the night. It is a chapter so exciting that one shudders even in daylight on the safe road above. Few books have had their origins so carefully recorded as has Treasure Island. We know that its genesis was a wholly fictitious map that Stevenson once drew. We are informed of the story's progress from day to day until at last the sheets went off to London to be printed. But Stevenson never gave a precise location to the Admiral Benbow Inn, nor told where he got the couplet of verses that was bellowed so often by old Bill Bones.
* If you're wonder how Stevenson came to grief over the moon in Prince Otto, here's the passage from chapter 9:
Thence he proceeded alone to where, in a round clearing, a copy of Gian Bologna’s Mercury stood tiptoe in the twilight of the stars. The night was warm and windless. A shaving of new moon had lately arisen; but it was still too small and too low down in heaven to contend with the immense host of lesser luminaries; and the rough face of the earth was drenched with starlight.
In the evening twilight, a new moon should be setting, not rising.
