Entering via the park's north-west corner the first thing you see is the Riverbank Arena, home of the hockey. It's temporary and completely exposed. In the blistering sunshine it's gorgeous but in the rain, probably not so. A few hundred yards to the north a bridge crosses the river Lea. It was here that the violent Beast of Stratford was first seen. A month after London won the games, a 16lb Canadian goose was pulled under the water. Experts blamed a crocodile, or possibly an escaped python.
Next comes Park Live on its floating pontoon – a giant double-sided screen with raised banks for spectators on either side. The Velodrome side, to the north, is already carrying the moniker Hoy Hill. The opposite bank is still up for grabs. The Idowu Incline perhaps, if the triple jumper pulls through?
Over the bridge the jagged, windowless tarpaulin of the Basketball Arena looks an unpleasant place to be on a hot summer's day. In a few weeks it will vanish, possibly to reappear in Rio in four years' time after the organising committee expressed an interest in taking the building in its entirety.
To its left is the giant Pringle of the Velodrome. It has become a cliché to call it that, but the likeness is extraordinary. It is apparently the fastest track in the world and, we hope, Team GB's House of Gold. Behind it lies the BMX track. In keeping with the UK's cycling boom, as soon as Paralympics closes these will become the centrepieces of a Velopark, with winding bike trails built into the wooded areas around it.
The Universal Stage is next, a little bandstand for unsigned acts. There's no shortage of food stalls either, where you can buy waffles, crêpes, smoothies, Asian, sushi, salt beef, noodle soup, Mexican, and treats from the "Cadbury's Treat Kiosk." Here the park nudges the athletes' village. The flags slowly appearing over balconies have given it the appearance of a Costa del Sol hotel, and this is German territory. One room, eight floors up, is home to members of the German diving team, and the banner flying outside would get you slung from almost anywhere in Magaluf. Next door are the Bulgarians. And in the corner, a yellow disc on a blue background, which is not to be a live weather forecast but the home of the three-strong team of Palau.
On the walk east a short set of steps leads down to the wetlands, from where you get the most intriguing view of the park's most intriguing structure. The ArcelorMittal Orbit, built with £13m from the UK's richest man, was likened to a crashed roller-coaster when the model was unveiled, but from here it looks more like a novelty toilet plunger. Its central lift column, with its concrete walkways coiled round it like a constricting snake, presses down into the earth – the sort of thing an HG Wells martian might use to suck up humans.
And to the left, the stadium. From the outside, whisper it, it's a bit naff. It cost twice as much as Beijing's Bird's Nest, but such is the price of industrial-relations legislation. Up close it is wide and flat like a soup dish. If you pass round the back and strain to see over the three-lane road on which the Routemaster buses will carry athletes, spectators and the media around the park, you can see the warm-up track. This is the dark side of the Olympic Park, the bit where, like the moon, you lose radio contact with the rest of the Olympics.
Next is Britannia Row, an expansive area of food concessions dominated by a two-storey Seafood and Champagne Pavilion, where bottles of fizz go for up to £65. Next door is the Copper Box, the home of handball. With 7,000 seats a lot of the legacy hopes are pinned on this arena. Smaller than the O2, or Wembley, it is hoped it will become a venue for smaller bands, or more intimate gigs. But, like everywhere on the park, the transport links are not straightforward. Getting to Stratford station is easy enough, but you're not really even nearly here by then. The Olympic Park is the size of Hyde Park, which has seven underground stops dotted round its perimeter. This Park has just one.
In front of the Copper Box sits, by some measure, the park's outstanding piece of artwork – the letters R-U-N, in the 30ft-high mirrors, by Monica Bonvicini. To the right is the BBC's studio, the same glass box that sat below Table Mountain during the 2010 World Cup. The coverage from here will doubtless be stunning, not least because it cannot capture the 15 blue shipping crates it is sitting atop.
And then, a short stroll in the direction of the stadium to the east, behold. The world's largest McDonald's, three storeys high and with 1,500 seats – big enough to serve several hundred thousand Jamie Oliver-antagonising Big Macs. Behind sits the three-storey Prestige Pavilion, set behind a black central frontage like a giant tinted limousine window. Here the £4,500 three-course dinners that come with a ticket to the opening ceremony will be served.
And then you're on top of the architectural jewel of the park, Zaha Hadid's Aquatics Centre. The wings of temporary seating, with their exposed girders, detract from its undulating form, but it is an awesome structure nonetheless. From one angle it looks like the beak of a duck billed platypus, inexplicably dropped from a great height on to a multi-storey car park.