The US ports were not bombed but how we shipped goods changed.

The city docks were based around wharves running perpindiclar to the shore where ships could dock and longshoremen manpacked the goods off of the ships -- see http://www.alamy.com/stock-photo-historical-aerial-map-view-brooklyn-manhattan-bridges-east-river-waterfront-36261361.html for a pretty good example. They did not need a lot of flat land behind them to manage the goods as they were in small bundles that could be carted to various warehouses in and around the docks etc.

In the 60s we started containerizing shipping. Goods now came in massive ships that needed to be parked parallel to the shore and unpacked with massive cranes and stacked and stored and put on trucks and trains. You now needed deeper water close to shore and loads of space to deal with the container farm. See http://www.robertcampbellphotography.com/oakland.html for some examples of that works.

In most cases the net effect was that the ports slid to a nearby suburban point from the old docklands. IE, from Manhattan and Brooklyn to Newark or from San Francisco to Oakland or from Baltimore's Inner Harbor to the various Papsco River ports. This also effectively broke the longshoreman's unions -- in SFO's case there was a massive strike that sealed the move to Oakland for example. On the flip side it became significantly cheaper and faster to ship goods in many cases, benefiting consumers in general.

I can answer for London - there are two main reasons. My family are East End Cockneys, and many of them worked the docks in droves in their heyday, hence my knowledge.

Here's a map of the London Docklands - my family who worked the docks are from the Isle of Dogs. http://www.lddc-history.org.uk/transport/1tran2.jpg

The Docks were one of the worst hit places by the Blitz, for obvious reasons. Below I've linked you to a fascinating website called Bombsight - it maps every bomb dropped on London during the Blitz. Have a look at the areas you see in the map above, and you'll see the level of damage.

The cost of repairing the docks, like many of the factories in London (located in the East End predominantly) and the houses around the factories and docks that were populated with the local workers who were generally very working class and poor, living in already sub-par conditions, was great. If you walk around those areas of London, try to spot the houses in streets that aren't quite the same as the other Victorian, Georgian or Edwardian townhouses - chances are, a bomb was dropped there. http://www.bombsight.org/#15/51.5050/-0.0900

This isn't to say that the docks weren't active for several decades post war, because they certainly were! Just pointing out this as more of a contributing factor, and detailing it because I know quite a bit about it.

The second, and larger reason (and one that could too explain the other Cities!) is simply that cargo ships got bigger. They no longer fit in to the small and very old London docks - it was hardly possible to bulldoze the surrounding areas of central London to expand them, so the ships that were too large went elsewhere!