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Death Note maybe? Pretty light on the action and no real romance but I think it fits the rest of the criteria fairly well. I will also second the recommendation of Phantom:Requiem for the Phantom as I think it fits these criteria better than anything else. (I think I have recommended this series more than any other just because it seems to fill a unique niche that people are always asking for yet tends to be rare in modern anime.)
I have to disagree with the recommendation of Nanoha though. It can technically fit some of those criteria but overall I think the tone is actually the complete opposite of what you're looking for and I feel it has a very strong "invincible characters" theme.
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