John:
There are a number of reasons you're getting the results you're getting... or not getting.
A thirteen second exposure is a VERY long exposure. What type of tripod are you on?
Also, were these shot with the kit lens? Extreme shooting situations will typically show the weakness of lesser equipment. And, you want to keep in mind that lenses tend to have "sweet spots"... apertures were they are stronger, sharper, clearer.... and obviously, the opposite.
It is tought to shoot this sort of shot. Simply by nature, you've got lights that want to blow out your exposure and shadows that want to hide from your exposure. Often shots like this will be created by using a sandwich of multiple exposures.
Event the time of night will play into it. Underexposing at twilight can be effective... since the artificial lights will be subdued, you can underexpose the sky and manage the artificial light.
It's just a matter of bracketing and trying different shutter speeds and aperture settings to see if you can hit the right combination.
And don't think that a lot of this can not be controlled in post processing too.
The tripod needs to be SOLID as a rock. If that shutter is sitting open for 13 seconds, the slightest breeze can cause movement (ever so slight) and will accumulate and blur or soften your shot.
It ain't easy... if it was, everybody would be doing it.

Keep trying different things. Anchor that tripod... don't extend the legs all the way out... try some sandbags or something that will stabilize it.
Of course, a shorter shutter speed would help... but expose for the artificial lights. Get control of those first.
Good luck.
JT