Like others, in the UK I would recommend Duxford (obviously), the Shuttleworth Collection, Fleet Air Arm Museum & the RAF Museum Cosford. If your timing allows, go to the Shuttleworth Vintage Airshow on September 6th
https://www.shuttleworth.org/events/vintage-airshow/ This show highlights the collection with many of their aircraft flying.
As for the Fleet Air Arm Museum, previous posters have mentioned unique types such as the Albacore & Wyvern. The FAAM frequently rotate airframes off display into their storage facility, Cobham Hall. On my last visit (March 2019), both the Albacore & Wyvern (plus both Fireflys & both Skyraiders) were off display. The good news is the FAAM do Cobham Hall tours and there is one planned for September 3rd
https://www.fleetairarm.com/event/187.aspx You must prebook as the tours sell out, but the September tour does not appear to be on sale yet.
Cosford is one of my favourite museums, especially the Flight Test hangar, with many rare and unique jets
https://www.rafmuseum.org.uk/cosford/th ... n=AircraftI agree with old iron's opinion of the Science Museum collection in London. The airframes are utterly iconic, but I last visited in October 2019 and was very disappointed - scruffy exhibits, poorly lit, upper viewing walkway closed. The Supermarine S6B, for example, looked dreadful with big chunks of paintwork flaking off!
Of the smaller independent museums, Newark is head and shoulders above the rest (and "smaller" is probably the wrong word to use about Newark!)
http://www.newarkairmuseum.org/Enjoy your trip