Could you give this wonderful place a worse German name, at least for English speakers who don't…read morespeak German? Because who wants to visit a rat house market? But while Haus does mean "house," and Markt does mean "market," Rathaus doesn't describe a house for rats--although locals might consider its primary inhabitants to be rats of a sort--and there's no actual market here. Rathaus is the general term for "city hall" (Rat meaning "advice," in this context), and I guess they're using Markt in a kind of general way to mean plaza or square. So just think of Rathausmarkt as "City Hall Plaza" in English.
And what a plaza it is. When I was an exchange student in Hamburg, the Altstadt area around city hall was where I wandered around a lot, got lost, regained my bearings, would get lost again, and finally generally figured out the confusing layout of this central part of the city north of the Elbe. When I returned years later, I found myself making the same mistakes I had made earlier on, but because I was older and (at the time) surer of my German, I was less worried about getting lost. I had done it all before.
It can be an intimidating place. There's usually a lot going on, and if the weather is nice and it's a weekend, it gets very crowded, and the sensory overload can be intense. I lied a little bit earlier when I said it's not a market, because they do hold farmers markets here on occasion, and there are permanent cafes along its edges.
As devastated as Hamburg was by Allied bombing during World War II--including many areas quite close to here--the Rathausmarkt survived relatively unscathed. It's a treat to stand in the middle of the square and look up at the absolutely gorgeous eastern facade of the city hall, with its copper roofs, clock tower, and iconic seal of the Hanseatic City-State of Hamburg. Like many European central squares, it feels beautiful and historic and alive at the same time. Its scale befits its importance as the main gathering place near the seat of government of a German state,* but it also feels human.
The only thing that keeps me from giving the Rathausmarkt five full stars is the general sense of foreboding I still have when it's extremely crowded. Not long before I came to Hamburg for the first time, my exchange partner's little sister, who was not that much older than ten at the time, was walking through a crowded Rathausmarkt when a stranger exposed himself to her and tried to grab her. Luckily, she was able to get away quickly, but she was still very traumatized whenever she was near the plaza, even with her father and older brothers around her. She was a brave kid (and is a wonderful mother now). I have never felt personally unsafe here, but I could never get her terror out of my mind, especially the first time I saw her start to tear up nearby.
Sorry to end on such a low note. It really is a beautiful plaza.
*Hamburg is both a city and one of sixteen German states, so it has a state parliament rather than a city council; technically, its Rathaus is a capitol rather than a city hall.