http://fallout.wikia.com/wiki/Museum_of_American_History
That contains both the hat and the gun. A little browsing yields the location of a recording of Lincoln's voice, several framed posters of significance, an antique Lincoln coin collection, and the "Action Abe" action figure (Abraham Lincoln with a katana).
I still think the DC brotherhood are a bunch of pansy's, why spend all that time and manpower helping out all these little settlements? The DC area is fucked no matter what those power armored boyscouts think they can do. If Maxson was still around he would have had that idiot Lyons shot.
If you played the last DLC, the waning power of the DC brotherhood still manages to neutralize the Enclave threat with your help. So even if they're on the decline, you get a MiddleEarth-esque "go out with a bang yo" through Liberty Prime.
Fuck yeah! DC Brotherhood for best faction in Fallout 3 - (Hay guize, we have this giant robot, who should we fuck with it?)
And yeah, first time I fired with the MIRV I blew myself and all my companions and 10 supermutants to shreds (with increased spawn mod). It was pretty awesome.