Okay, here's my recommendations, in order:
1) The American Museum of Natural History in New York City.
BUT, only shortly behind...
2) The National Museum of Natural History in Washington, D.C.
3) The Royal Tyrrell Museum of Palaeontology in Drumheller, AB. While the
above two are in major cities with plenty of else to do, and to which it
is quite easy to travel, the Tyrrell is a bit harder to get to (fly into
Calgary, drive for an hour and a half to the little town of Drumheller).
However, given that, these are phenomenal exhibits of Late Cretaceous
Canadian fossils, and are smack dab in the rocks whence the fossils came!
(I heard a rumor that at the 1988 SVP meeting, the only one since '87 I've
missed, that Jack Horner was walking around the parking lot and came
across a hadrosaur jaw...). There are exhibits of other dinosaurs here,
too. For researchers on Late Cretaceous dinosaurs of North America, the
Tyrrell is Mecca, but that is as much for behind-the-scenes stuff as
anything else.