The apron opens up the possibility that his bolthole (or man-cave) was in the vicinity of Goulston Street if you put any stock in Jack the Ripper returning to his bolthole after murdering Elizabeth Stride.
Where was he going after murdering Elizabeth Stride? No certainties but could "bolthole" be among the tops answers. Catherine Eddowes' murder is generally understood as occurring as an afterthought; something that happened because he was unable to get what he wanted from Elizabeth. Did he meet Kate on his way back to his bolthole?
With blood on his hands and being in possession of a kidney, uterus, bloody apron, bloody knife and the alarm of the police on the streets of the East End... what's the probability that his bolthole was actually back in the vicinity of Buck's Row or Berner Street? Meaning, what was the purpose of trekking to Mitre Square if his bolthole was on the other side of Whitechapel in an area he had just come from [45 minutes/an hour] earlier?
He could have continued westward from Mitre Square after murdering Catherine Eddowes, thru City of London. I'm sure there were plenty of doorways in that direction where he could leave her apron. But, the aspect of the apron has him doubling-back and/or stagnating in the vicinity of Mitre Square and Goulston Street, lending to the idea that he had reached the neighborhood of his bolthole.
there,s nothing new, only the unexplored