The Region Around Avonlea
This is the rough map I've put together, based in the clues mentioned below, which are taken from various of the Anne books. (See note on the format of the references.)
The map uses a 'browser-safe' palette, so you should see roughly the same colours that I do. The orange/brown lines are roads, the black ones are railways.
Three roads meet near Avonlea - from Carmody, Newbridge and White Sands. This is where Avonlea village hall stands (AoA, ch 2, 1st page). Similarly, three roads lead from Cavendish to New London / Stanley Bridge, Rusticoville and North Rusticoville. The first thing must be so see which 'real life' place corresponds to which fictional place.
It is eight miles from Avonlea to Bright River (AoGG, ch 2, 1st page). Bright River is on the main line to Charlottetown, whereas Carmody is on a branch line (AotI, ch 3, 2nd page) that was not built until some time after Anne's first arrival in Avonlea, about the time she was at Queen's (AoGG, ch 35, 1st page).
Avonlea is generally reckoned to be identifiable with Cavendish. I am assuming that the books are largely compatible with the coastline, roads and rail around Cavendish. I am also assuming, to begin with, that the places named in the books are mostly re-namings of real places. Occasionally the text seems to require a settlement in a position not marked on my map, and here I have simply put it in the most plausible place. On the whole, this seems to have worked quite well as regards 'Avonlea' and the district around it to a radius of about 12 miles.
The evidence I have noted from the text, and the conclusions I have drawn, are as follows:
The most likely candidate for Bright River would appear to be Hunter River. The only other possibility would be Kensington, which is on the far side of Avonlea from Charlottetown and would involve doubling-back unnecessarily.
East Grafton is about 10 miles from Avonlea (AoA, ch 8, 2nd page). Six miles from Spencervale to Avonlea (COA, ch 2, 10th page). Paradoxically it is ten miles from Avonlea to Spencervale (AoA ch 18, 3rd page). This suggests that we should not be too worried about making the maps correspond too precisely with the text as regards distance. Let's say that the distances are as people reckoned them before modern road-maps and mileage markings. Two miles from Bright River to Spencervale (COA, ch 2, just at the end of section 5 - "the September chapter"). Two miles from East Grafton to railway station, presumably Bright River (COA, ch 7, two pages from end of chapter). It is four miles from Newbridge to Green Gables (AoGG, ch 2, 8th page).
The road from Bright River to Avonlea goes through Newbridge (AoGG, ch 2, 8th page). The most logical candidate for Newbridge seems to be Rusticoville.
Spencervale could be identified with South Rustico. More likely, perhaps, that it is (unmarked on modern map) at cross-roads between Bright River and Newbridge. This would fit better with the six-mile distance from Avonlea.
On the road to White Sands, the sea is on one's left hand side. Therefore White Sands must be to the East of Avonlea (AoGG, ch 5, 5th page), which would identify it with North Rusticoville. If this is so, then Carmody must be New London, since that is the third of the roads meeting at Avonlea (AoA, ch 2, 1st page). This is supported by a reference to 'Carmody harbour' (COA, ch 3, 19th page). Carmody therefore on the coast. From the map given in the diaries, there are two villages between Cavendish and New London: Bay View and Stanley. In the journals (vol 1, p 230, 31 Dec 1898) LMM describes Stanley as the place where they most often went to buy supplies. May therefore be worth trying Carmody in the position of Stanley. This is a more reasonable distance for walking (AotI, ch 22, 2nd page). When Matthew goes for the doctor (AoGG, ch 18, 3rd - 5th pages) he goes first to Carmody and then to Spencervale. Suggests, though doesn't absolutely require, that Spencervale is further than Carmody, but in the same direction. Will stick with the present position for now, however.
White Sands is five miles from Avonlea (AoGG, ch 5, 1st page). Problem: '... she goes on to White Sands station' (AoGG, ch 1, 6th page). If there is a railway station at White Sands, why do people from Avonlea go all the way to Bright River to meet the train? Perhaps the service to White Sands is very infrequent. It is difficult to see how a railway could get to White Sands except by going via Spencervale, yet there doesn't seem to be a station at Spencervale, whose inhabitants have to go to Bright River for the train (COA, ch 2, just at the end of section 5 - "the September chapter").
On the other hand, there is the fact that White Sands gets a lot of visitors (AoGG, ch 5, 5th page) and has a hotel (AoGG, ch 33, 5th page) where 'rich Americans' stay, which makes it more likely that it would have a railway station. Referring back to the modern map, I see there is a road crossing the river mouth at North Rustico (= White Sands). I thought of putting a railway following roughly this route, by-passing Spencervale and going on the opposite bank to Newbridge. In the end, I left this out, as the balance of probabilities seems against there being a station so much nearer to Avonlea than Bright River, given that Bright River is the station the Green Gables people always used (until the station at Carmody opened).
White Sands is on the way back from Charlottetown to Avonlea (AoGG, ch 29, 7th page). This suggests that it is somewhat further south than I have it on the map. It cannot be where I have Newbridge, however, as this would not agree with the description of the three-way junction at Avonlea (AoA, ch 2, 1st page). Perhaps Mr Barry had a particular reason for going via White Sands on this occasion, despite it being apparently a little longer than going via Newbridge.
Coming from Bright River, through the White Way of Delight, the sunset sky is visible at the end of the tunnel created by the trees. Therefore the road must not be too far from E-W at this point. It does not have to be exactly so, since it is the 'sunset sky' that is visible, not the setting sun itself. The White Way of Delight is shortly before getting to Newbridge (AoGG, ch 2, 8th page).