Few points
Richard was born in the Midlands and spent much of his earlier life following the traditional progression around his parents many estates.
On his brother's accession to the throne he was probably housed with his brother George in and around London - he did not move into Neville's care until the mid 1460s when he was a teenager (almost an adult by the standards of the time)
After the Neville's fall from favour his marriage meant he took control of the Neville's northern holdings and spent much of the 1470s acting as the main focus of Royal power in the North.
Although his father was Duke of York - York itself and much of the area was strongly Lancastrian though the Wars of the Roses and it was only Richard's influence in the 1470s as the main focus of power and patronage in the area that saw it switch its loyalties.
Precisely. And he showed particular favour to the city of York, additionally referring to the area as "home". The incidental fact of his Midlands birth is now being used rather disingenuously to downplay this association with Yorkshire and the north, which was previously accepted by any historian with no horse in the race. I was born in Bristol, and for six years lived there, which is more time than Richard would have spent at Fotheringhay, but I certainly don't consider myself a Bristolian. In these parochial arguments about family origins, attempting to reinvent him as a "southerner" or "midlander", people often ignore the fact that both his parents were raised at Raby Castle in County Durham - and his paternal grandfather was born and bred at Conisbrough. He was no less a "northerner" in his origins than anything else, and he spent much of his adult life in the north, the only monarch to do so. This is why people still care.
Given his brother's household was largely dominated by people based in the Midlands and South on his accession Richard was forced to rely very heavily on his northern supporters who were already in receipt of his patronage - which gives the added impression of Richard as a "northern" king but in that he had little choice. Had his reign lasted and people came to terms with his rule it is more likely that his household would have become very different over time and less reliant on a small section of geographic support.
But that didn't happen, did it? This is a bizarre argument: "we know he did x,y,z, but let's suppose he had lived longer, he might have changed, so that fact in itself is of more importance than what actually happened." :-)
As to his funeral and burial
1) York Minster's dean and chapter have made it absolutely clear it did not want to be drawn into the arguements over the burial and had the University of Leicester asked them the likely answer would have been no.
2) Royal burials had been at Westminster until Henry V's in 1422. Edward IV had rebuilt St George's Chapel at Windsor and clearly intended it as his resting place (where he and his wife were both interred). There is no evidence that Richard intended to be buried at York (despite his chantry chapel plans) - he might have preferred St George's or the family's memorial (to their father) chapel at Fotheringhay.
3) Traditionally deposed monarchs or those killed in a battle (as Richard was) were usually buried in a nearby religious institution (as he was given Leiceister didn't have a cathedral at the time).
York Minster *was* drawn in and named as an interested party in the court case. We don't know what he "might have preferred" in terms of burial, and can't possibly presume to guess, but the favour he showed York Minster was on a par with what his brother was doing at Windsor.
Monarchs may have been buried in a nearby institution, but many were subsequently moved, as we know for the examples of Richard II and Henry VI. Once you've exhumed someone, all bets are off. We know this from the Romanov example.