If I can make the magic work, I'll embed a map here. More likely I'll point at one. But you can have some pictures anyway.
View River Walk in a larger map
We started from Westminster station, more-or-less at the foot of the Big Clock Tower that's not really so big.
You can't see them in the picture above, but there are floating lights in front of the dock that you can see on the right of the building, each topped by a golden crown. I do wonder who has the job of cleaning them
From there we crossed the Westminster Bridge, which is patently one of the big tourist spots - the buskers and street performers were dense on the ground, and the tourists even denser. Yes, there are people dressed as the Queen hanging around at Boadicea's feet, waiting for tourists to give them money to have their photo taken. Making it even worse was that they were all wearing truly creepy Queen Elizabeth II latex masks.
Half way across a piper was playing his heart out, somehow largely ignored by all the passing tourists.
On the other side of the river we headed east toward, and past, the London Aquarium, the Eye, Southbank Center, Hayward Gallery, National Theatre, the Tate, and (eventually) the reconstructed Globe theatre. Along most of the walk, the lamps had these strange dragon/carp bases, oddly Eastern, but primarily resembling mer-Pugs
More of the street performers lurked in the underbrush on the south bank as well, feeding well of their natural prey. There were a lot of strolling tourists.
The tide was out, and the mud flats on the bank were exposed, looking a good deal cleaner and less unsanitary than I would expect. Further along, past Blackfriar's bridge (the one in the photo below), families were down on the mud, picking their way along, probably looking for cockles. I'm not sure whether this indicates that the water is clean, or whether it indicates that Londoners have evolved a tolerance for toxic sludge.
Oddly, there was a short stretch of sand, presumably artificially introduced, and two enterprising sand sculptors had set up shop, waiting for tourists to toss coins down to them. I would have been more inclined to give them money had they created something more impressive than a Sand Couch to lounge on.
Having strolled for almost an hour, we gave up and strolled across the Millenium Bridge (apparently held up by Science! and Advanced Engineering!), up toward St Paul's. Even if it needs a good clean (and to not be so damned expensive to visit), it's an impressive building.
We turned left and strolled down toward Ludgate (the spot where they used to hang folk. And quarter them. And disembowel them.) and found an Earl of Sandwich shop, bizarrely decorated with pictures of James Cook and Joseph Banks, then jumped on a tube and nipped up to Oxford Street before coming home.
A worthwhile walk.