I've always thought an action figure or toy museum would be a great idea. Especially if you could get into a position where there was government support (though this could be difficult, unless you could really get them to believe that these action figures had the same kind of artistic or historical significance as the contents of other museums), or could get space in a building that was already owned.
Or you could follow the example of Forrest J. Ackerman, who was basically the prototype for what we would consider the modern "fan", and ran a museum out of his home.
http://en.wikipedia.org/wiki/Forrest_J_Ackerman
I think action figures and toys have enough of a rich history to certainly make a wonderful museum out of them, with enough potential for rotating exhibits to keep things interesting basically forever. The problems I could see would involve the overhead of such a museum, the neccessary traffic year-round for it to be a worthwhile endeavor, and the cost of acquiring new pieces.
I suppose if it were something that was done "art show" style in the beginning, with small, well promoted exhibits at a helpful gallery or exhibition place, and if there was a lot of support from the fan community both in terms of attendance and donation of pieces, that it could be done, however.
