I am about to watch Sin City: A Dame to Kill For.
I have absolutely no memory of the first movie. 9 years does that sometimes.
Is it important to watch Sin City 1 before Sin City 2? Do I need a recap?
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Yes. The film acts as both as sequel and prequel. From the wiki:
Miller said the film would be a prequel and a sequel with interlinking stories both before and after the first film. Miller, who was writing the screenplay in 2006, had anticipated for production to begin later in the year.
The new elements of the movie are discussed here, in article that was written before the film was released (so contains no spoilers). To quote from the article:
Miller has said that the new film is based primarily on his story A Dame to Kill For (the second in the series of books). This one centres on Dwight (Josh Brolin) and takes place years before his storyline in the first Sin City film (The Big Fat Kill – the third in the series of books), and before he needed the facial reconstruction surgery which made him look like Clive Owen (who plays him in the first film).
It also states:
One of the storylines is based on this short story, collected in the book Booze, Broads & Bullets, which is the fifth in the series. This is Marv’s story...
Along with the original stories, there will also be two new ones written by Miller especially for this film. The Long Bad Goodnight is Joseph Gordon Levitt’s chapter, while The Fat Loss picks up with Hartigan and Nancy where the first film left them. So, anything goes basically – characters that appeared in the previous film could return, and we won’t be surprised if others come to an unexpected end...
As you can clearly see, there are stories taking place both before, during and after the original story - so watching the original would definitely help.