The first fossils found attributed to T.rex were a couple of teeth found in Golden, Colorado in 1874 by Arthur Lakes. However, these were not recognized as T.rex teeth for a while, so I can understand if you don't count that(although I do).
The first skeleton(CM 9380) was found in 1902 in Montana, so based on your options, I'll say Montana, although I'd argue it was in Colorado.

(CM 9380 on display in the Carnegie Museum of Natural History in Pittsburgh, PA. It's an estimated 11.9 meters long and 7.3 tons in weight).
"Men like me don't start the wars. We just die in them. We've always died in them, and we always will. We don't expect any praise for it, no parades. No one knows our names."
―Alpha-98