Sounds like Inverted World by Christopher Priest. Of course, try to find it in a bookstore...
But then, try to find a bookstore.

Yes let's ruin the planet even more... It's not a good idea...

they had something looking very similar to this is the ridiculous disney movie john carter. only it had massive pylon looking legs upon which it crawled along . legs look way cooler than these tank belts. also , if one of the legs malfunctions you can lift it to fix it while the whole city is moving without having to stop for maintance. if one of the tank tracks malfunctions, this entire moving city will then need to stop most likely.
the bigger an object is, the more energy it will require to go from rest to motion. the initial inertial energy requirements are so large with a device like this, that once it's moving , it needs to stay moving until it stops as planned. an unplanned stop could spell disaster if the city operates on a limited energy budget and an uncertain supply of energy from external sources.
how about this. look at the russian nuclear power electricity generating barges that were designed and built only recently for the purpose of powering up and bring online offshore oil platforms.
that barge is towed by a boat . if that boat had wheels, legs, paddles, or a propeller that was electrically motored, ( like a modern diesel train is ) than if that boat were capable of hoisting upon itself and cradling a 300 megawatt barge and operated on that much energy. then you're looking at a nuclear powered amphibious moving city. with a few hundred people on it. and an operational range anywhere on planet earth that won't overheat or over-chill it.
oil platforms are 'moved' . but for comparison.
550,000 deadweight tons http://en.wikipedia.org/wiki/Pierre_Guillaumat_(supertanker)
on land you have the http://en.wikipedia.org/wiki/Crawler-transporter carrying far less than any ship, which floats its cargo. and uses no more than 10 megawatts at peak operational loads.
300 megawatt nuclear reactor should be sufficient to power a city in motion ( especially if you shut off all nonessential city systems while in motion )
you'll probably want to go with legs. yea, legs. the real issue is how to design legs to operate properly in coastal mud and sand.

Is it really that far-fetched? Nomadic humans could pack up and move their entire village to follow natural resources. Sheep-herding, horse-herding, buffalo-chasing, etc.
A natural resource apocalypse is coming just as surely as mankind can produce offspring faster than the earth can replenish those resources. This concept could very well be a variation of one of history's repeating themes - a future Earth crawling with roving bands of Tech-nomads.
Another of history's repeating themes is that we discover how to solve future problems through failure to achieve current ambitions. Much of the ideas involved in creating one of these tech-nomadic cities comes from ideas inspired by the challenges of space-colonization.

He rebelled against "Do something useful."

integrate it with a 100% sustainable effort and I think it would be quite a project.

Coastal dwellers may want to live on one of these in the near future.
Sea-level rising? Tsunami coming? - "roll-out".

Yep, Inverted World. I have the paperback. Bought it in a used bookstore in '98.

... and what would they be walking over? Land already wasted by some other walking city?

Catamaran? Put it on water and cruise :)