When you say that cost isn’t an issue, do you mean that your parents can pay the full cost of Duke? I agree with the advice to run the NPC and then talk to your parents about whether or not they can afford to pay what the calculator says.
I agree with UCBalum. If you have to ask the question, you don’t have a clear first choice, and you shouldn’t apply ED.
However, Duke is one of the few schools who does admit that applying ED does give students an advantage in admissions, so here’s my take:
My opinion is that most students would be happy at a variety of colleges. It’s not like there’s one true “soul mate” college at which you might be happy, and all others would make you miserable; you might have a different experience at Duke but not necessarily a less fun one. So when you are making this decision, don’t worry about whether Michigan might be marginally better; worry about whether you think you’d enjoy the experience enough at Duke to make that a good choice for you.
Why do you love Duke? It seems to check almost all of the boxes - smaller classes, warmer weather, live on campus all four years, a strong sports culture - mostly centered around basketball, but strong in other areas too, good Greek life (30% of young men and 40% of young women join Greek organizations), and a pretty well-reputed social life. You will definitely find a lot of nerdy students at Duke because it is a very selective school, with a 10% acceptance rate and students who are admitted because of their high academic achievement. But any school that you consider with high prestige will also have a lot of nerdy students. Nerdy, however, does not mean socially awkward or that they don’t know how to party or are uninterested in Greek life or sports.
Do you think you would be happy at Duke? If you got accepted tomorrow and were told that you’d have to go there, how would you feel? Sit on that for a few days and think about it. Honestly, it sounds like you’d be fine with it, so as long as your parents are able to pay the full costs and don’t need to compare costs, so I don’t see why you shouldn’t apply ED. But if you are really torn and it’s tearing you apart, then don’t apply ED - just apply RD.
Also, are you from Michigan?