I'd like to include this connection (containing Uffizi, Hermitage etc), but am looking for a good definition for 'famous' to set boundaries (as any city at least has one museum). Any ideas? Is there some 'Three star Museum List' or Top 20 best museums in the world...?

I think famous is sometimes the best available definition and for our (non-scientific) purposes it should be satisfactory.

These should give you something to go on! The English word "Prestigious" might help


http://www.berro.com/world_best_museums.htm

http://uk.askmen.com/fashion/travel_top_ten/54_travel_top_ten.html

http://www.worldreviewer.com/experiences/specialist-museum/

I note that Els has listed this "Connection" after the above discussion - but I wonder if Plantin-Moretus really fits the bill of "Prestigious" or "Famous"? It seems to me that it is what I call a "niche" museum. I won't pass comment on whether it should have been inscribed as I haven't visited it. I accept that the subject it represents is interesting/worthwhile and potentially "inscribable" but its inscription has as much to do with the nature of the Building and its historic use as to the collection inside it.
Rather like "Libraries", the collections inside Museums on their own don't seem to meet the criteria for WHS inscription (there being different lists for such "movable objects") and hence their "inscription" is either
a. to some extent accidental from being within the boundaries of a more widely defined site
or
b. Due to the nature of the building itself -of which the "collections" inside may be an essential and historic part

A problem is that the word "Museum" has a very wide meaning such that almost ANY historic building open to the public could be so called - but isn't this "connection" more about major "collections" which happen to be within an inscribed area and may not be "self evident" from the inscription itself? I feel that collections which are an essential and historic part of the building's main and original purpose are not really what this connection is about

To show that there is no "Nationalistic" favouritism I would also leave out Greenwich - it is not primarily a "Museum" in the "housing a collection" sense - only in the same sense as all historic buildings open to the public are

I would also leave out The Vatican as its "collection" is an essential part of its "Universal Value". The ceiling of the Sistine chapel is part of the building also and the other paintings/tapestries etc are as per its prime purpose

The Hermitage comes into my "grey area" for this connection - The Building is clearly part of inscribed St Petersburg as a "Palace" but I think the collection within IS separate enough from the building's original intrinsic purpose to justify this connection. Much of what can be seen there has been added after the Revolution (eg all the Impressionist/post Impresionist works) and is not part of its role as a place to display the royal collections. The building has ceased to be "a Palace which houses a collection of Royal items" and become a "Museum which was a palace and now houses a collection whose importance goes beyond the building's original purpose". The same arguments would apply to the Uffizi and Louvre.

I got a bit carried away after the third weblink that you provided above.... but had bad feelings already when adding The Vatican. The 'best fitting' ones I think are Uffizi, Hermitage, Pergamom and Louvre. Others in that category would be the British Museum, Prado, some museums in the USA (if they would be located within the boundaries of a WHS).

People now have suggested:
- Venice: Accademy Gallery
- Florence: also Bargello National Museum, Palatine Gallery and Saint Mark's Museum
- Rome: Capitoline Museums, National Roman Museum, Doria Pamphilj Gallery and National Gallery of Ancient Art

????

I agree with your "best fitting" 4.
Beyond that the problem is to avoid totally opening the floodgates! But didn't I suggest the "connection"!!

As for the others - well as I understand it they are all "collections" which are not there because they are inextricably linked to the building's original purpose so they fit my criteria for a "Museum"
A number of those suggested are Art Galleries. In English an Art Gallery and a Museum are different things - but I suppose that, strictly, an Art Gallery is a type of Museum and, if you tried to split then you would then have problems with joint institutions!.
If the list grows to 20 or 30 then does it matter - The ones suggested are all potentially of world significance. I can add no more!

I think one can simply include every major museum within the bounderies. This leaves out smaller/ less significant museums, but still lets us include some museums that are perhaps not the most renowned in the world but still exhibit significant works/objects. I agree with Solivagant that the distinction between the building and its content is vital to this connection.