Sorry for the delay Russ. Life has been a rat race recently and I just got out to try a few shots and get some settings for you. I went into Cadillac and they have a train that is part of a city park. The train was part of the lumbering times from years gone by. For the record, I shot this with a tripod and long shutter. I was shooting close so was using a wide angle lens and was trying to protect my depth of field so also shot a higher Fstop to accomplish that.
21mm focal length
2 seconds shutter
Since you were trying to take pictures "on the fly" I looked for a house with some reasonable lights to shoot and see what I could come up with. The biggest thing to remember, cameras settings are always a balance. The lower ISO numbers give some what cleaner images on average but they require a lot of light. To shoot we need a minimum shutter speed to keep camera shake to a minimum. That means for most people with a camera that has a form of anti-vibration programing you will need at least 1/30 shutter speed to even start hoping to not blur the shots. That said, I took a few shots that came out reasonable from the road, with a quick stop and shoot out the window only.
80mm focal length
1/60 Shutter speed
This one was shot right off the side of the street using my wide angle zoom.
40mm focal length
1/60 Shutter speed
I was shooting with a DSLR. The 80mm was shot with a 70-200 and it is a LARGE lens with vibration reduction. (second picture) It was braced on the window of the car from inside. The third shot was completely hand held with a wide angle lens that had NO vibration control. Now a point and shoot may not be able to give you quite the settings I used but they do give a base line to work with. Now, if your lens will not get down to an f4 like this picture, you will need to compensate by raising ISO even higher or lowering shutter speed to allow the same light into a smaller (larger numbered) fstop setting. As you can see, I shot with a 1/60 shutter speed. If your lens is a 5.6 minimum, you might try shooting at the 3200 ISO but shoot at 1/30 of a second if the camera has vibration control built in. IF you look at your picture that you posted, I pulled some of the camera information from it. Your settings were:
Exposure Time = 1/15"
F Number = F6.3
Exposure Program = Manual
ISO Speed Ratings = 1600
Focal Length = 35.1mm
I do not know if your camera will handle ISO 3200 (lets in double the light as the 1600 setting) or if you can drop your fstop back to 5.6 and bump your shutter to 1/30th but if possible, that may give you a cleaner shot with better edges. The problem you are facing is that most lights on houses only put out a very small amount of light. Adding more daylight MAY cause the lights to be less bright looking. It all depends on the look you are trying to capture. Since full darkness is where the lights show their strongest, that is the direction I took. Our eyeballs attached to our brains work in combination to bring in light and provide balance and details through I think it is 6 or 7 shade levels of light. The camera can reproduce about 4.
So what we see can not be recorded perfectly by any camera. In good light, the difference between our eyesight and what the camera records is so close that we do not notice many of the differences. BUT, take pictures in dark environments, that is always a challenge. IF there is a possibility, shooting from a tripod opens more possibilities then hand holding. Pretty sure I am preaching to the choir but for the benefit of all reading, I am just covering the bases. If I can be of more help, let me know.