I think it is better to put the four sentences into one. In fact the first is not a sentence.
This city is not the cleanest in the world, not the brightest nor the most beautiful, but it's something.
Is this good?
This city. It's not the cleanest in the world. It's not the brightest and certainly not the most beautiful. But it's something.
I think it is better to put the four sentences into one. In fact the first is not a sentence.
This city is not the cleanest in the world, not the brightest nor the most beautiful, but it's something.
I am not a teacher or a native speaker.
Perhaps:
This city is not the cleanest, not the brightest, and not the most beautiful, but there is something special about it.
Not a professional teacher
Or but it is really something.