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Well, one of my favorite anime is "Case Closed".
Admittedly, it plays in the present time and this whole relationship/"I'm a kid again" stuff can be a bit awkward but 95% of time it's just about breaking the case. It orientate itself defnetly to Sherlock Holmes and other great detective storys and has many allusions. The settings are also very attractive and you will experience a lot about Japan. The cases are very interesting and ingenious. It defenetly has the classic sherlock holmes vibe!
Another famous detective anime is "Lupin III" but I never watched it so I can't say much about it.