When discussing the reputation of Babylon in the Bible, its extremely important to remember that the old testament was written by jews, who would have had ample reason to hate the Babylonians. When the Babylonian king Nebuchadnezzar took Jerusalem, he expelled many Judeans from their ancestral holy land. It was an insult that cut deep, and would not soon be forgotten by the jewish people. Its hardly surprising that Babylon is described with special distaste by the jews of the time. As for whether or not their negative reputation is deserved, its a bit of a difficult question to answer. Much of the old testament was completed between the sixth and fourth century BCE, and at this time Babylon had existed for over a thousand years. They would have had a long history, and the ancient world was a brutal place. You'd be hard pressed to find a city that had existed for over a thousand years in this time period, that hadn't done at least a few things to upset their neighbors at some point or another. If you want to know how other civilizations thought of the babylonians, ask yourself, how do we think of germany? Would you have given the same answer in 1945? In 1910? In 476? How the nearby civilizations perceived Babylon at any given time, would have depended on the recent interactions between Babylon and the civilization in question. You would have undoubtedly found people who admired it, despised it, or were indifferent towards it, for a vast multitude of reasons. It was a cultural center, with famous architectural features and was in many ways a wondrous city, but it was also at times quite powerful. Powerful states have great armies, and armies seldom do their job without upsetting some people. What the civilizations around Babylon thought of it would have really depended on who you asked, and when.

As for whether or not the bad reputation of Babylon was deserved, it comes down to a matter of opinion. There's no such thing as an ancient government or city state that was purely benevolent. Warfare in the ancient near east was common, and brutal. By modern standards, you could probably point to a multitude of instances in Babylonian history when they behaved violently or ruthlessly. If however, we grade the Babylonians on a curve, there's nothing particularly nefarious that makes them stand out from the crowd. Look at this quote from the Assyrian king Ashurnasirpal II, who lived about two centuries before the Babylonian exile of the jews.

"I built a pillar over against the city gate and I flayed all the chiefs who had revolted and I covered the pillar with their skins. Some I impaled upon the pillar on stakes and others I bound to stakes round the pillar. I cut the limbs off the officers who had rebelled. Many captives I burned with fire and many I took as living captives. From some I cut off their noses, their ears, and their fingers, of many I put out their eyes. I made one pillar of the living and another of heads and I bound their heads to tree trunks round about the city. Their young men and maidens I consumed with fire. The rest of their warriors I consumed with thirst in the desert of the Euphrates."

When you see that other civilizations were producing rulers like this, does it really make sense to single out a specific city as being particularly mean? The ancient near east could be a truly violent place, anyone looking for examples of bad PR concerning any one of the civilizations within would find ample examples. But taken as a whole, there is nothing in my mind that would distinguish the Babylonians as particularly brutal as compared to their neighbors.