I'm from Yorkshire and lived in York for ten years, so I say York.
There's a very good museum to Richard in the walls of York.
His son is buried in Yorkshire, at Middleham, and they lived in Middleham Castle for a long time. They always went back to Middleham when they needed to relax and get away from court.
The only claim that Leicester has is that is where he was killed. He was killed near there because that is where the two armies met. It could just as easily been Nottingham or Warwick or anywhere in the midlands. Most kings are not buried where they were killed, but somewhere with some connection to them.