I see from the BBC website article which can be read here, as well as from various newspapers, that the dispute over where to bury the remains of King Richard III has now reached the courts. I think the Judge wise in what he says.
There is no evidence I can think of that Richard ever wanted to be buried in York before, and still less after his accession to the throne. His Queen Anne lies at Westminster, and the ambitious plans for a college of chantry priests prove nothing conclusive to my mind - as Desmond Seward pointed out in his book on the King (one by a man previously pro-Ricardian who changed his mind and concluded that King Richard was guilty as, largely, charged) Richard was very prone to establish chantries for those whose deaths were or could be taken to be his responsibility. He appears to have wanted to be sure they were indeed resting in peace.
In my opinion Leicester is the right place for his remains - he has been there since 1485 and a dignified new tomb in the Anglican cathedral is a rather better place for a King of England than under a car park.
There is now the risk that the remarkable technical achievement of recovering and identifying the King's remains together with all the genuine historical interest and insight that has generated is going to be obscured by groups or individuals pursuing their own idiosyncratic agendas.