Wittenberg, with Luther's Statue: Hamlet. Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Apart from the statue of Luther, this Market Square probably looks as the town would have looked around 1502, when the university which Hamlet supposedly attended was founded, and where Luther soon initiated the Reformation from which Hamlet's puritanical attitudes are derived according to Shakespeare's choice of background for him. This is a totally different environment from Old Hamlet's, into which Christianity is barely filtering according to his allusions, but the first coming of Christianity to Northern Europe had an impact comparable to that of the coming of the Reformation to the same area many centuries later, and Shakespeare typically synchronizes these two parallel eras in his plot.
The plausibility of these ideas is reinforced by the views of David Davalos commenting on his new play “Wittenberg":
“I’ve always been intrigued by the fact that Shakespeare identifies Hamlet as a student at Wittenberg, Marlowe cites Faustus as part of the faculty there, and history puts Luther there, teaching, preaching and launching the Protestant Reformation. There’s clearly a reason why Shakespeare and Marlowe sought to connect their creations with Luther’s university . . . . I felt that might be an interesting story, and could address issues of the interplay of reason vs. faith, issues that are still with us today.” Orlando Sentinel Theatre Blog: 14 February 2008