I suggest the location is around the end of the alley called 'Marine View', or the corner of Tyrell and Wolfe St, or the grounds of the Grammar School.
The sketch map is ambiguous and tricky to interpret.
Firstly, here is a reading I think to be wrong, and then why, and then an explanation that makes everything more coherent, as a way to explain why I think it's the right one:
It looks like Elliot & Constable are coming from the crest of the hill towards the church, 150 yards away (~137m), with the path to the Farm/Town* on their right, and Kirby killing Burigon at about 50 yards (~45m), on the other side of the path to their approach and the hill. The James Meehan 1818 map, has a road leading directly from the front of the church to the market garden. If the murder was 50 yards from the church (which is in the same spot as the current cathedral), on the other side of the path to the Hill, the site would be around the corner of Newcomen and Church St, a block up from the Grand Hotel. But that is likely wrong because it contradicts other information.
The police account (SRNSW: SZ 792 COD452B
Court of Criminal Jurisdiction Case Papers Nov/Dec 1820 Part II
pp. 496-519 Map page 507) indicates the action took place 'behind the church'. This could be literally at the rear of the church, facing East, but none of the other maps, paintings or accounts match with this. This most likely means more generally 'behind' relative to the settlement, and in a painting of the church overlooking the settlement, it is seen to face the settlement, so it would also be to the rear of the church though at more of an angle to the side (as you would say in the settlement 'up behind the church on the hill' rather than literally, if you stepped out the Church's back door).
They met the Aboriginal people bringing in the escaped convicts from the bush. This accords with somewhere further up the hill or over it facing West. The accounts mention an Aboriginal camp, with the Burigon and others bringing the captive convicts from that direction. This is most likely at the top of the hill or nearby, as it accords with all the other information and is evidenced, in the W. Preston painting of early Newcastle Aboriginal people showing camps directly on top of The Hill: https://governmenthousebarracks1804.wordpress.com/about/ (it might seem strange to have a camp high on an exposed hill, and also that the most convenient path to 'the bush' was up a steep hill, but at that time, the suburbs inland from the high ground around Cooks Hill were marshes, and there was no fresh water, so people would have stuck to the river and the high ground near the beaches.)
The pathway drawn is then perhaps not the *road* depicted in the map leading straight from the front of the church to the garden, or town, nor the ring road, but another well worn *path*. It's reasonable to think there was a more establish road to the church, due to the high traffic expected on Sundays and people wanting to ride horse or buggy to it, since it's so steep. A path not shown on the map is one of the most prominent features in the Lycett painting of Newcastle, https://livinghistories.newcastle.edu.au/nodes/view/11518 thought by some to depict Wallis, a convict and Burigon himself (in about the exact location he was murdered - if painted after the murder it might have been a poetic gesture, but the painting is dated 1818, and the murder was 1820), and leads towards the farms near Newcastle beach. This path matches the alignment in the sketchmap of the path leading towards the Farm, between the Church and the crest of The Hill.
So the most likely point is further up The Hill from the church.
But it doesn't make sense that the search party approached from the top of the hill which seems to be what is shown in the diagram, because the narrative describes them coming from the settlement and going behind the church to see the Aboriginal people and convicts approach from the bush. It doesn't make sense that they would somehow end up getting in behind the convicts and Aboriginal people. Cartography is a discipline and people have to learn to draw maps accurately showing everything from above, and some smart people still struggle with that at school. Naively drawn maps, often mix up angles of view, icons, and drawings of things from the side - just as the church is drawn side on, and possibly back to front (this is still a bit troubling, but nothing at all makes sense if it is understood as a literal drawing, so it's probably just an icon meaning 'church' - a person familiar with a place might not even remember which end the steeple was on when put on the spot - for Newcastle residents, are you sure you know which side the Cathedral steeple is on without looking?). Yet a European familiar with maps, might try to emulate official maps, especially when in an official situation, like court proceedings - so we can expect this map to be a jumble.
It's likely then that the lines from the names Elliot, Wells and Menslowe at the bottom do not indicate their position and movement down the hill, but are merely labels with lines pointing to where on the map they were standing when the murder occured about 150yards up the hill from the church, near the pathway, with Elliot and constable being about 50 yards from the murder.
It would be important to indicate their positions and proximity, to prove they could see what they say they saw in their witness statements.
So I imagine the act of drawing the sketch map goes like this: It was up on the hill. Draw crude hill from side on (naif maps almost always depict a hill this way). About 150 yards from the Church, draw an arbitrary church with a steeple. There's the pathway leading down to the farm. The murder was here. Elliot and Constable were here about 50yards from the murder. The drawing becomes crowded, so a methodical way of indicating positions on the path and The Hill is introduced with names at the bottom and lines to where they were, and arrows to reinforce the point that this person was up there.
All this considered, the murder being near the old path depicted in the Lycett drawing, about 150yards up The Hill from the church around the end of the alley called 'Marine View', the corner of Tyrell and Wolfe St, or the grounds of the Grammar School.