Where to start with Athens? Firstly, there’s more to the place than the rock of the Acropolis with the Parthenon on top, you know. Though I did appreciate that my hotel room looked right across to it.

I was in Athens for the opening of the New Acropolis Museum, of which more later. But on these occasions, we all like to explore. So I walked, and walked – according to my step-counter around 20 km a day. That’s normal but in this case, with temperatures of some 33 degrees and humid with it, I found that city-exploring was like being in a sauna. I was losing a kilo of weight a day. 

On my walks I found interesting things such as the city’s heritage of Byzantine churches and chapels. Or the rainwater downpipes shaped like serpents’ mouths. Or the fact that – as in India – you can sometimes find a whole family of four on one motorbike. And there are some evocative bits of non-classical dereliction like the hallway to an abandoned house I encountered behind a rusted gate, complete with rusting spiral stair and cat. 

Of course I went to the Parthenon, where the sorted stone fragments of the masons, arranged in heaps, are almost as fascinating as the great temple itself and its various outbuildings, which are all forever being restored, dismantled and reassembled. But the main reason for going up there was to look down at the New Acropolis Museum below. 

This is the big, important new cultural building which announces to the world that Greece is now world-class when it comes to the display and conservation of its own artefacts. It was a famous competition win by architect Bernard Tschumi - Swiss-born, with offices in New York and Paris. 

Tschumi always sports a red scarf - and even in this choking heat he was wearing one, albeit a lightweight chiffon number. And the museum?  With its top floor - the Parthenon Gallery - skewed and proportioned to align with the Parthenon itself, and each floor below that given a distinctive character, it’s a bit like some giant ice-cream wafer. Or would be but for its black sun-cheating glass. 

The building hovers on columns over the revealed archaeological excavations of Athens’ merchant city, visible from the approach route and beneath the glass floors of the lobbies inside. 

It’s an earthquake-resistant building made of great fat concrete columns (and more delicate stainless-steel-clad columns on the top floor). The sequence of interior spaces, and the arrangement of the artefacts, is a great deal more successful than its somewhat enigmatic exterior. The double-height gallery of statues and sculpture fragments, which you can wander among, is terrific, as is the way the beautiful caryatids of the old Erechthion temple – as lovely and graceful from the back as from the front – gaze down the interior hill of the entrance ramp. 

But what everyone’s talking about of course is the Parthenon Gallery on top, displaying the parts of the Parthenon frieze owned by Greece – along with plaster casts of the large parts of it that are in the British Museum, where they are known as the Elgin Marbles. 

On opening night, both the Greek President and Culture Minister issued pleas for the return of the Marbles to this, their new home. It is certainly a most powerful argument for reuniting all the surviving pieces of this, one of the greatest works of sculpture than mankind has ever produced. 

Just before I left, I went for another walk in the steamy heat, this time into the semi-wasteland of the new commercial district behind my hotel. And there I stumbled upon a vast 2005 bank HQ building by another Swiss architect, Mario Botta. Who might be thought something of a neoclassicist. But in this context, he can’t really compete.