The basic problem is one of large dynamic range. The range is higher than normal daylight shots because the light sources are in the picture, and you want to resolve their details.
You therefore address this as any other large dynamic range problem. The first approach is to expose so that the part of the highlights you care about end up just at the end of your sensor range. The dark parts then fall out where they fall out. With a good sensor, there can be enough dynamic range captured that this is all you have to do.
If you're not wasting range above the bright spot and there is still too much noise in the dark areas, then things get more complicated. HDR (high dynamic range) techniques require taking multiple picture. One puts the highlights at the end of the sensor range as before. Take one or two more, each 2 f-stops more exposed. The highlights will clip in those, but more detail will be captured in the dark areas. Clever software then picks the best parts from each frame and makes a composite with good detail in both the highlights and the dark areas.
According to this method, your first image is still overexposed as can be seen here:
The highlights are still blown out. I'm just guessing, but to capture them acceptably you want at least one EV less, probably two.
However, in your case you have another problem, which is camera shake. This is evident everywhere, but is particularly easy to see by looking at the trails left by point light sources:
The solution is to hold the camera more steady and/or use a faster shutter speed. A tripod is a obvious thing to use in this case, since your scene isn't moving and a slow shutter speed would give you other advantages in picking the exposure. It is also necessary if you end up using multiple-image HDR techniques.
The highlights in your second picture look worse than in the first picture because they are more blown out, and just as wobbled:
To see where you're at with using a single image, here is a section of the first picture with non-linear brightening to show detail in the dark areas:
You can see reasonable detail in the dark areas, but splotchiness is starting to be evident. This can be see particularly on the dark smoke stacks. However, this example above is from post-processing your 8 bit image. There should be considerably more dark detail available in the raw image.
Given all the above, it may be possible for you to get what you want from a single shot. Use a tripod, and try 1 EV less exposure than your first picture, then see what is really available in the raw file.