Where is she buried.

[Maiden Stone]

There is a Wellington St. in Prestwick, adjacent to the boundary between Ayr and Prestwick burghs.

Just looking at an old OS map and if it is adjacent to the old Heathfield hospital then the parish boundary is to the north of it running along Heathfield Road.  Will try a better map

The Wellington Street I mentioned in reply #3 is on a modern street map. It's north of Heathfield Road and directly behind Heathfield Primary School, so just inside Prestwick Burgh. It leads off Waterloo Avenue. That Wellington Street is parallel with  Afton Avenue which is a continuation of Hunter's Avenue.
Could the 2 streets which have been named Wellington Street have been connected in the past?
The area between Ayr Burgh and Prestwick Burgh was Newton-on-Ayr Burgh until late 19th century. The area in the southern part of Prestwick was known as New Prestwick.
I suggest beginning a search in Ayr, Newton and Prestwick parishes.

[Maiden Stone]

I've checked several old maps and the thinking is;  Hunter's Farm just north of the parish boundary and in Prestwick, had a road leading to it from Newton on Ayr.   It was locally known as Hunter's Road, then to honour The Duke of Wellington for saying that a horse is worth more than a Scotsman, they renamed the road as Wellington Street.  On that map was showing the County Buildings and Gardens in front, but the place was un-named.  So, at some point they have named it Wellington Square and probably around the same time renamed Wellington Street as Hunter's Road.

Also looking at old maps on National Library of Scotland  website.

One inch Popular edition 1921-1930; Ayr and Kilmarnock sheet 78; 1926 map, surveyed 1923.
The road which is now Hunter's Avenue terminated at Heathfield Road, beside the hospital. There was a gap and then there was another road which terminated before the boundary between the 2 burghs. The road on the Prestwick side of the boundary might have become the present -day Afton Ave.
https://maps.nls.uk/view/74400717

19th century maps. The road which is now Hunter's Ave. terminated at the the road which is now Heathfield Road. A short road or track led from the opposite side of Heathfield Road to Hunter's Place. Heathfield Primary School now appears to occupy the site of Hunter's Place.
1st edition 1856-1871
https://maps.nls.uk/view/74488585
2nd edition 1885-1900
https://maps.nls.uk/view/74488586

 

[Ian Nelson]

Check my previous post as I've now changed the map attachment to show Wellington Street, Newton-on-Ayr and the nearby Cemetery at the end of Russell St, cheers, Ian

[Maiden Stone]

Ian Nelson reply #11. That's a strong possibility. The area was demolished and is now late 20th century flats.