asked for anime/manga I would rec for 11-year-olds and why. That is a tough question! It really depends on the kid and what their reading level is, as well as what their interests are. And since I know you're asking for your daughter, but don't have any specifics other than age, I will go ahead and rec what I would have liked at that age. (But if you want to give any more specifics in the comments, please feel free!)
If she likes mysteries, I would recommend The Kindaichi Case Files
and Case Closed
. Both are murder mysteries, though Case Closed is more cartoonish. Case Closed also has an overarching plot about the main character drinking a potion that turned him into an elementary school kid (he's actually a teenager) and trying to find the people responsible.
One thing I really love about Kindaichi is that the murderers are not just evil bad guys out for money or serial killers. They always have a reason and they get a chapter or two at the end where they tell their story about why they had to get revenge on these people. It's very sympathetic to them while still showing that murder is not the right way, and they often try to commit suicide at the end (some may succeed, I don't remember) and are shown being regretful of what they've done.
Case Closed's tone is a little ligher (as I said, it's often cartoonish and has Wacky Hijinks), though the cases are still mostly murders. The cases are also a lot shorter, usually just one person is killed whereas Kindaichi cases usually span a couple volumes and all feature the cast getting stranded somewhere where people are picked off one by one. With Case Closed, there are also some cases solved by Conan and his elementary school friends (who unlike him really are little kids) that are not the big murder mysteries.
Obviously it depends on how mature your daughter is whether or not she would be able to handle these, but they are aimed primarily at junior high/early high school aged kids in Japan, so the target audience is not too different.
One thing is that Kindaichi was not fully released in the US and is out of print, so it may be hard to find. The cases pretty much stand alone, though, so if you find some and not others, you can just go with what you have. Case Closed seems to be doing well in the US and has dozens of volumes out (with about 80 out in Japan).
Another great mystery series is Young Miss Holmes
, in which Sherlock Holmes has a ten-year-old niece named Christie who also solves crimes. IIRC most of the cases follow the original Holmes books but with Christie added (she doesn't solve them instead of Holmes, but follows her own clues and usually arrives at the same conclusions, that sort of thing). If you're thinking this series is a total Mary Sue fic, you're right, but it's well-written and really enjoyable. Holmes and Watson are pretty much background characters and it's just Christie and her awesome maids having adventures. This is aimed at adults, but I don't think there's anything in there that would be unsuitable for kids.
For something totally cute and light-hearted, I really love Yotsuba&!
and Chi's Sweet Home
. The former is about a very imaginative five-year-old girl named Yotsuba who lives with her dad. Each chapter is titled "Yotsuba & [topic]" and focuses on some new discovery or adventure of hers. She gets a bike or goes camping or plays with the neighbor girls. It's heartwarming and charming and hilarious.
Chi's Sweet Home is the story of a kitten who wanders off from her mother and gets adopted by a family with a little boy. It's told entirely from the kitten's POV and is all about her adventures.
Both of these manga are aimed at adults, but are enjoyable for all ages.
Oh, I've just thought of another one! If she likes time travel and post-apocalyptic wastelands and psychic kids then Psyren
would be right up her alley! It's really cool and I know kid!me would have loved it (I imprinted early on Alas, Babylon and Time Bandits, and even earlier on Escape to Witch Mountain, so kid!me would have seen it as the ultimate combination of all of those).
Of course for adventure stuff there's the big Jump series like Naruto, Bleach, and One Piece. Of those my favorite, hands-down, is One Piece
. There's also Sailor Moon and Card Captor Sakura in the magical girl genre. To be honest, I've never read Sailor Moon, but it's a classic. I did enjoy Card Captor Sakura
If anyone else has recs, please feel free to chime in in the comments!