I am very much in favour of a Museum of Toronto of which the City, in addition to the other ABCs, would contribute artifacts and knowledge. A TTC museum, free standing and charging the sort of admission typical of such venues, would be interesting if a site could be found for it, but with a separate subsidy allocation from the City's Culture budget rather than anything the farebox touches. Random hoarding of artifacts, dribbled out to the public when the whim takes the Commission, I do not care for at all.
The alternative would be a Technology Museum, linked to the Ontario Science Centre, showcasing land, sea and air vehicles built in Toronto/Ontario. After all, the story of the Toronto transit vehicle is often a story of Ontario more broadly - Orions from Mississauga, subway cars, streetcars, GO trains from Thunder Bay, SRT cars and some streetcars from Millhaven, maybe some locomotives from London?
And hey, it would be a place to park Newmarket's BYDs...