For my current role they asked me what I was looking for, I gave them a number that I was happy with and they came back offering a bigger number so didn't need to negotiate anything up this time round.
I had the same thing, I didn't really know an accurate number despite doing as much research as I could. I gave a number 20% more than what I expected the higher side of the mean for the position and area was, expecting to negotiate down to the middle somewhere. They offered 10% higher than my request, to me the money was plenty high enough so I saw no reason to negotiate further although I knew I could probably push higher. Perhaps at the end of my first year I ill push for a 10% increment.