There's a large collection of instruments of all sorts and from different ages in St Cecilia's Hall in Edinburgh: this includes the various keyboard instruments: fortepiano, spinet, harpsichord. The non-keyboard stuff used to be in The Reid Hall, next to McEwan Hall, near Bristo Square, but I think it was moved to St Cecilia's when it was expanded, and the other hall re-furbished.

And, as with the Brussels museum that JoeG describes, the Cite de la Musique in Paris has a similar way of hearing the instruments as you go around: very impressive.