Le Bourget. Back when I was a frequent visitor, you more or less had to be a francophone to navigate it, but according to
@SnapRoll all the placards now have English translations.
(Also, back when I was a frequent visitor, I had to be kicked out at closing time.)
With the annexes allowing much more room for display, the Smithsonian is now more like Le Bourget, but if you'd asked me in the early nineties, having lived in D.C. only a few years before, I would have put Le Bourget far ahead in terms of the breadth of the hardware displayed
(and also the access to it) vs. the Smithsonian's location on the Mall. Of course a lot has changed since then for the Smithsonian, for the better. And even then, the Smithsonian may very well have held the edge in terms of its archives, I wouldn't know. Not being an accredited historian I never got anything more than a brief tour of the Smithsonian archives, but I expect it would be easy to lose years in them.
Kansas Cosmosphere is also a treat, though heavily biased to the "space" side of "aerospace." It's a great space museum. On the "aero" side, they do have an SR-71 . . .
I hope to visit the Air Force museum in the next few years. A friend was there a month ago and was amazed by it.