Title pretty much explains it. I heard some different things about this like Nazis were planning to make Oxford capital of Nazi UK etc. But is there any proof or anything that this is actually true or just a myth?
That does not seem to be likely. This theory was raised, most popularly, by Stephen Hawking in Black Holes and Baby Universes and Other Essays.
I was born in Oxford [in 1942] ... Oxford was a good place to be born during WW2. The germans had an agreement that they would not bomb Oxford and Cambridge in return for the British not bombing Heidelberg and Gottingen. It's a pity that this civilised sort of arrangement couldn't have been extended to more cities.
While I wish to discredit neither Mr Hawking's immense achievement in his specific field of expertise nor the inspirational value of his life as a whole, he's not a historian and an anecdote raised in the autobiographical part of a popular science book is not in itself a valid historical source.
I mostly speak from the German side due to my area of individual expertise of course, but I have never seen anything coming close to a Luftwaffe document that justifies Mr Hawking's anecdote. The Luftwaffe assessed targets by their value, be it economic, industrial, military, or cultural - albeit this independent assessment was sometimes overwritten by political interference (famously including Hitler's reaction to the 25 August 1940 Berlin air raid). The reason why Cambridge and Oxford were spared was because there were bigger fish to fry. After all, what's more important to the war effort: a university city or an industrial hub?
Likewise, Heidelberg and Göttingen were minor cities in Germany and were neither resource hubs nor industrial centers nor logistical chokepoints, rendering them unimportant targets. The Allied bomber commands simply had more pressing targets - industrial centers, armament factories, major railway centers, hotspots of coal and steel production, et cetera.
And still, Göttingen was actually attacked by air eight times. Quite infamously, three explosive removal experts were killed by an American bomb in Göttingen on 1 June 2010. Unexploded bombs dropped during World War II continue to be a semi-regular event in German major cities, and these three heroes were tragically killed in their attempt to keep civilians safe from the unexploded ordnances, or, as we Germans euphemistically call them, Blindgänger.
And, finally, to challenge the overall notion presented by Mr Hawking's anecdote, such a 'gentleman's agreement' between the warring parties of World War II would have been completely at odds with the ideological fundamentalism that both sides approached the necessity of the other's defeat.