I agree with Andrew on this matter, having read five Barrie biographies (including Andrew's, of course!) and having given interesting matters such as this much thought while researching for my own little book.
Assuming we are talking about the writing of Peter Pan the play: if JMB started work in November 1903, and finished his first draft of the play in March 1904, then I would say all the work on the play up to that point was done at Leinster Corner. I would say most of his writing was done in his study at his London home, where conditions were constant, distractions were few, and where he maintained his library.
In the autumns of 1893 and 1894, however, when Barrie did not have a permanent home, he did spend weeks at a time working at his sister Maggie's home at Medstead, Hampshire. This included a period of a few weeks within a couple of months of marrying Mary Ansell; they both stayed there in early autumn 1894, and again in December that year, after an intervening few weeks in lodgings in Fowey, Cornwall. At Medstead, Maggie built a study for her brother, but the extent to which it was used later is not known - it has long since served as a bedroom.
From 1895 to 1900 the Barries had a London home only. From 1900 to 1909 Barrie had the occasional use of his wife's leased cottage, Black Lake Cottage. However, his visits there were usually only for entertaining and holidaying. These occurred at times between April and September. He had wanted a study in the pine woods behind the cottage but he never got it. He had a desk in one of the bedrooms there at around the time of Peter Pan's creation. There was a study at Black Lake Cottage but it was not built until sometime after Barrie wrote Peter Pan. (Certainly not built by 1905, and possibly not until around the time the Barries divorced, in 1909, after which Barrie never went there again. But it was certainly built before 1912, and therefore possibly only used by Mary (Barrie) Cannan and her new husband Gilbert Cannan). That study has also long since served as a bedroom, despite the many alterations and 'improvements' to the building during the twentieth century.
However, whereas work done on Peter Pan the play, after March 1904 and up until December 1904, again was probably done at Leinster Corner, I think there is a possibility that some of it may have been done at Black Lake Cottage also. Consider this:
We know that whereas Barrie, as usual, spent August 1904 at Black Lake Cottage, and in fact stayed there through to the end of September that year, unlike the three previous years he did not have the considerable distraction of, or preoccupation with, frequent, if not daily visits from the Davies family and games with the Davies boys. Since 1902, privately, Barrie and his wife led pretty separate existences despite being married and living in the same house. They were both holidaying at Black Lake Cottage for August and September of 1904, but they each did their own thing for most of the time: Mary working in her beloved 'happy' garden, James walking their dog Luath or shut in his room, thinking and writing.
So maybe some of the work on Peter Pan was done at Black Lake Cottage. After all, could the author have put this work to one side for two whole months, when the play was due to open within three months? Somehow, I doubt it. But I guess we will never know.