I'm a huge fan of Berlin. My 5th annual May trip to Berlin got shot down this year by Coronavirus. I like being there early to mid May. There are many daylight hours to see things and temperatures are generally mild.
The amount of WWII stuff depends on how deep you are willing to dig. There are the big things like the Reichstag, Topography of Terror, some old Nazi buildings around Topography of Terror, a grassy space where Hitler's bunker was. A little further afield are things like the German-Russian Museum at Karlshorst that contains the room mentioned above where the Germans signed one of the documents of surrender to end the war (and contains an exhibition that gives the Russian victor's history of WWII) and the highly, highly recommended Gleis 17, the track at Grunewald station that was the deportation site for Berlin's Jews -- each transport train is memorialized with a metal grate on the platform that contains the train's destination and number of passengers. Even further out are Sachsenhausen concentration camp and Ravensbrück, a female concentration camp. Or how about Berlin Underground's tour of a WWII bomb shelter, which is near a partially-collapsed Flakturm (anti-aircraft tower) in the nearby Humboldthain Park. More obscure are things like the Kammergericht building, which held The People's Court, the tribunal that tried political enemies of the state, in front of whom 17-year-old Helmuth Hübener, after being sentenced to death for distributing anti-Nazi pamphlets, declared, "Now I must die, even though I have committed no crime. So now it's my turn, but your turn will come." Or the Plötzensee Memorial, which consists of a monument and the shed where political prisoners (including Hübener) were put to death via guillotine or hanging from meat hooks. Even more obscure is the Bonhoeffer House, the home of the parents of Dietrich Bonhoeffer, one of the few German theologians to oppose the Nazi regime and the place where he was arrested by the Gestapo; there are tours on Saturday mornings that consist of a short talk on his life and then a walk up the stairs to his room, which houses some of Bonhoeffer's belongings. The Bonhoeffer House is a short walk from the Grunewald station through a pleasant neighborhood built in the early 1900's and relatively spared of Allied bombs. More obscure? The memorial for employees of Siemens who died as soldiers during WWI and WWII outside the company's headquarters (which is near a very interesting 1930's housing development for Siemens employees that is part of a UNESCO World Heritage Site).
Cold War highlights for me: The Berlin Wall Memorial (Gedenkstätte Berliner Mauer) with an area of the wall as it originally existed, the enormous Soviet War Memorial in Treptower Park, Checkpoint Charlie (not for the silly fake checkpoint or the actor military dudes who are supposed to no longer be there, but as a historical site where US and Soviet tanks faced off in October 1961), the Schöneberg Rathaus where JFK spoke, the TV tower (Fernsehturm).
Transportation + WWII + Cold War Coolness = Tempelhof Airport. Built largely by the Nazis. Used by the US and the UK for the Berlin Airlift. English tours available -- more are available in non-COVID times than are currently available. https://www.thf-berlin.de/fuehrungen/english-guided-tours/
Outdoor spaces I like ("scenery"?): The Tiergarten, especially the Luisininsel with all its flowers; Volkspark Friedrichshain with its fairy tale fountain, its two hills made out of war debris, and its large number of Berliners being Berliners; Britzer Garten -- the tulips in the front and the rhododendrons in the back are blooming in early to mid May.