Like someone else who said this earlier - "I think there has to be a democratic agreement on what is right and proper for the final visible burial of a historical figure so bound up in a nation's sense of heritage " - I think it has to be York, but if not York then somewhere nationally significant and meaningful to the person whose remains they are.
ZebraOwl states above that the archeological practice of re-interment close to the place of exhumation is 'good practice' but in the event of finding a nationally important historic figure - which to be honest, the University were really not expecting to find: only Philippa Langley and her Looking for Richard project and John Ashdown-Hill pushed them into doing this, along with the one-third emergency funding by Society members - in the event of finding a nationally important historic figure and anointed king, the exhumation licence terms should be set aside for a process that should take into account lots of other factors.
I think Leicester feel as if the long-term tenure that happens to have occurred with his remains (as with any remains buried in a place) means they have the moral right to assert the remains should stay there.
But surely the most important thing is - where would this King wish to have been buried? And the answer is NOT LEICESTER.
He might have wished to have been buried in York Minster - his endowment to the Minster to found a College of 100 priests to say masses for him and his family, suggests this may well have been his intended mausoleum. It cannot be proven - he left no known will - but since it is the church he spent most money on (and the churches he spent significant money on regarding Collegiate status were all in the north), it is suggestive that he wished to be buried in the north and in York in particular. If not York, then he might have wished or expected to be buried in Westminster Abbey alongside his wife (where now there is no precise location for her burial-site and standing room only alongside Henry Tudor), or possibly St George's Chapel Windsor, alongside his brother Edward.
What he would not have wished is to be buried in the place where he was slaughtered, his body despoiled and displayed for shame and mockery and maliciousness, and then hastily buried in an inadequate grave, naked, with no coffin or shroud and quite possibly with his hands tied.
This should not be a question of which town or region loved him more, which one is more deserving of tourism or whether Leicester is in the heart of his kingdom: it is a question of where do his remains belong? Where is it most respectful and honourable that they be re-interred, possibly taking into account what he might have wished for himself? As a king who spent much of his childhood and adult years in or associated with the north, it makes good sense to bring him back to the north.
Some people claiming descent from his family-line are stating for York publicly and may well (I hope) mount a legal challenge to the archeological licence, on which a coroner might decide. The Mayor of York, an MP for York, the City Council are determined to press ahead for their case, even though York Minster are acquiescing with the Leicester option (it's not exactly seemly for cathedrals to be setting themselves against each other). Yet York Minster has some responsibility not just to itself as an edifice (a big challenge financially etc to take on Richard being re-interred there), but also as the cathedral church of the entire northern province of England, it has a duty to respond to the desires of the people it serves. If many people in York and Yorkshire and the north of England (let alone all those from the southern province and from Wales, Scotland etc) are requesting that York be the place where this lost king is laid to rest, I don't think it is reasonable of them to simply refuse.
Considering that it is only five days since the remains were publicly identified as Richard III, I find it disheartening and patently wrong that all the decisions about his remains have been wrapped up as a fait accompli by the involved parties, with no public or wider consultation.
Anyone who wishes to continue supporting York as the place for re-interment, please sign the e-petition and ask anyone you know to sign it too. Anyone with an email address and a residential address in the UK can sign it, ie several members of one family.
epetitions.direct.gov.uk/petitions/38772