I am looking at a birth certificate for 2 November 1946:
For where born it it says Duncan House U.D.
After some research I did find this:
https://archives.bristol.gov.uk/records/43207/9/12/352
Where can I find out more about this building?
As you know, it is difficult to give a good answer to unspecific "I want to know everything/anything" queries, so I will answer with some questions and ideas for further research.
Methodology for researching buildings is not unlike researching people. They are constructed and sometimes demolished and so have 'birth' and 'death' dates. For tips on how to get started, try the #HouseHistoryHour website, particularly the Moments page for the section Getting Started and Top Tips.
If you want to know about Duncan House for context to support family history research and you are particularly interested in the 1940s because of the birth certficate, one strategy might be to search the British Newspaper Archives around that period to see what is being said about the house.
The National Library of Scotland holds a book Records of Duncan House School, The Promenade, Clifton, Bristol (1973) which may be of interest.
TNA's Discovery shows Bristol: Duncan House School, archive reference ED 109/8792/10, as part of 109 - Board of Education and successors: HM Inspectorate: Reports on Secondary Institutions (record not online) with an estimated date range of 1946-1955.
Given the time frame, I was also curious whether Duncan House was re-purposed for some institutional use during wartime, and had not yet been returned to use by the family that might have owned it. However, the results at TNA suggest that there was a school named Duncan House as early as 1933.
Notes on Registrations
I am curious about the certificate's notation of Duncan House U.D.
findmypast has this information about the abbreviations used in the 1939 Register:
Borough/district – This refers to the enumeration districts used in 1939. Those outside of London include various abbreviations after them:
R.D – rural district
U.D – urban district
M.B – municipal borough
C.B – county borough
Duncan House may not have had its own district in the 1939 Register, but it is not unusual in the US for large institutions to have their own Enumeration Districts in census records. Still, I wonder why the certificate says "Duncan House U.D." and not simply "Duncan House". In the 1939 Register, Bristol is the name of a C.B. (county borough).
UKBMD's page for Bristol Registration District has a list of subdistricts (including Clifton) and of the parishes included in the district, but there is no correlation (they don't say which parishes are in which sub-district). However, that list of parishes might give you a way in to other resources.
A table of adminstrative areas pertaining to Bristol can be seen via A Vision of Britain Through Time.
See this related question on the RootsChat forum: Birth Certificate U.D. meaning?.
The building still stands, at 20 Clifton Down Road, and normally I would expect the UD to mean Urban District would assume that the registrar probably just forgot to write the district name before it.
It's a bit odd though because as best I can figure out in 1840 Clifton would have been in the County of the Town of Bristol and would not have been in an Urban District.
Indeed it seems Urban Districts didn't exist before the Local Government Act 1894 so it's hard to see how it can mean that!
