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 dark blue line is the stream. The blue areas are ponds. The green areas indicate rough contours - the darker, the higher.
The road from Newbridge crosses over the Lake of Shining Waters (AoGG, ch 2, 10th page). Barry's house is off the road, on a hillside with trees behind, on the far side of the Lake of Shining Waters, as you approach Avonlea. Green Gables is near but approached from other road. On the other hand, the alternative route from Green Gables to Barrys' house - across the (frozen) Lake of Shining Waters rather than through the Haunted Wood (AotI, ch 18, 2nd page) - suggests that the Lake may be to the north of the Barrys' house. The 'Blythe orchard' is on the 'far side' of the Lake of Shining Waters, the context apparently indicating the north side (AoGG, ch 17, 4th page; see also ch 38, 6th page). Probably it is also on the east side of the road, because the Barrys' House is on the west.
On the way back from Bright River, after crossing the Lake of Shining Waters, Matthew and Anne have to go up a hill (AoGG, ch 2, 11th page) before reaching the junction of the roads (which is probably in the valley on the other side). The cemetery is on this hill (AoGG, ch 38, 6th page). When coming back from visiting Matthew's grave, Anne goes past Gilbert's house.
Anne's bedroom is in the East Gable (AoGG, ch 3, 3rd page). Therefore the view (AoGG, ch 4, 2nd page) across the meadows towards the hill, through a gap in which the sea is visible, must be roughly Eastwards.
The description of the homesteads in Avonlea (AoGG, ch 2, 11th page), with Green Gables towards the left as one looks from the main road, and the star over it being in a SW direction, fits if Green Gables is south of the road that goes West from Avonlea. There is also more room for the woods behind Green Gables than if it were off the road going East. In this position it also makes sense for Anne and Diana to go to the Kimball Place (AoA, ch 21, 3rd page) through the woods behind Green Gables. If Green Gables were to the East of the Newbridge Road as I originally thought, there would have been no reason for them not to have gone by the road.
Mrs Lynne's house commands a view of all roads out of Avonlea (AoGG, ch 1, 1st page), therefore probably quite close to where the three roads meet. The brook that runs past Lynde's Hollow originates in the woods behind Green Gables. Green Gables is 1/4 mile up the road from Lynde's Hollow, not including the distance up the Green Gables lane (AoGG, ch 1, 3rd page). This supports the assumption that Lynde's Hollow is not far from the cross-roads. Green Gables is approached by a narrow lane, presumably roughly parallel to the Newbridge road. The back-yard is on the west side, and is entered from the lane. Therefore the lane passes Green Gables to the west, though presumably doesn't go right past as there is nowhere for it to go because Matthew built it as fa r from the road as possible. The kitchen windows look both east and west. The brook is visible from the east window (AoGG, ch 1, 3rd page).
Lovers' Lane runs off westwards up into the woods from the lane leading up to Green Gables (AoGG, ch 15, 1st page). It leads to the brook, over a rustic bridge. Dryad's Bubble (AoGG, ch 12, 5th page) is the spring by the log bridge over the brook. Victoria Island is probably some way upstream of Dryad's Bubble (AoGG, ch 20, 3rd page).
William Bell owns a piece of land across the brook from Green Gables (AoGG, ch 13, 3rd page). Andrew Bell owns the woods overlooking Violet Vale, beyond Willowmere (AoGG, ch 15, 1st page). Willowmere is a small round pond in Mr Barry's field. To get to it you go through his back field (AoGG, ch 13, 3rd page). Idlewild is a small ring of white birches in William Bell's land across the brook. On the way to school, Birch Path through Andrew Bell's wood comes after Violet Vale (AoGG, ch 15, 2nd page). The Haunted Wood is over the brook on the way to the Barrys (AoGG, ch 20, 4th page). Presumably a bit further up the hill from William Bell's field. After the Birch Path, you cross the Newbridge Road (presumably South of the Lake of Shining Waters) and the school is on a hill overlooking the road among spruce trees with a fir wood behind (AoGG, ch 15, 2nd page). The church also overlooks the Lake of Shining Waters (AoGG, ch 11, 4th page). Perhaps the church is next to the school, which they would probably have used for Sunday School.
There is a possibility that you pass to the North of the Barry farm (Orchard Slope) to get to Violet Vale and Birch Path. This would put the school nearer the junction of the three roads that meet in Avonlea. There doesn't seem to be enough room this way - and it is supposed to be 'dusty and hot' (AoGG, ch 15, 1st page) in summer, which seems to imply a reasonable distance.
There are two roads to Carmody from Avonlea. I'll assume that the modern main road is more likely to be the lower road and that the upper road lies to the south and east of it (further inland). The upper road is less direct. Harrison's house is on the Carmody Road (AoA, ch 6, 11th page).
Mr Harrison is Green Gables' new 'right-hand neighbour' (AoA, ch 1, 2nd page), which suggests a position to the east. But the Harrison farm 'adjoins [GG] to the west', so its position on the map is OK. Must be 'right-hand' looking from the road, not from GG (see also AoA, ch 2, 3rd page).
Hester Gray's garden (AoA, ch 13, 6th page) is some way out of Avonlea, facing south, sheltered by trees to the north, somewhere south of the upper Carmody road. It is within a mile of Green Gables.
Relation between Kimball Place, West and Middle Grafton, and Echo Lodge (AoA, ch 21, 3rd - 4th pages). The Kimball Place is about 4 miles from Avonlea, on the road to West Grafton. You get to Middle Grafton, coming from Avonlea, if you to too far to the left. Echo Lodge is on the way to Middle Grafton, about 3 miles from the Kimball Place.
'Mr Kimball from Spencervale' (AotI, ch 5, 7th page). Suggests that 'the Kimball Place' (AoA, ch 21, 3rd page) is in or near Spencervale. Not conclusive, since there might be other Kimballs elsewhere. Present map has Spencervale between Bright River and Newbridge, with the Kimball Place several miles away on the Carmody road. Is there a more consistent arrangement possible?
Ten miles from Kensington to Avonlea (COA, ch 4, 1st page). Kensington here referred to by its 'real' name, therefore presumably not to be identified with any of the imaginary names such as Spencervale, Grafton, etc. This means that in the Anne books there are three places whose names are not changed: Charlottetown, Summerside and Kensington. (This assumes Kingsport is really Halifax, Nova Scotia, and not a real place).
Approached from the lane, Green Gables is seen against the background of the Haunted Wood (AotI, ch 7, 3rd page). Suggests that the wood may be somewhat further south than I have it at the moment. Cross check against original reference in AoGG (ch 20, 4th page).
These two routes also mentioned in AoGG (ch 18, 4th page) when Anne goes to Barrys' house to treat the croupy baby. In this case it is through the Haunted Wood (too snowed-up on this occasion) or the longer way 'through Lovers' Lane and across the field' (not described in any more detail). In both cases I would guess that the alternative route to the Haunted Wood is either north to the main road and then round by the Newbridge road or (perhaps more likely in the snow when there might not be much point in sticking to the road) cutting off the corner somewhat, passing round the (unwooded) north side of the two hills.
The Lake of Shining Waters is visible from the Green Gables lane just before the Yard Gate (AoWW, part 2, ch 5, 3rd page). This is a slight problem with the present map. Perhaps the woods between Green Gables and Orchard Slope are not on all that high ground. Perhaps the Lake is further to the north or the south, so that the woods are not between it and Green Gables.