Here's a little list I've been working on of Bond items on display in museums. Some of these I went looking for and some I stumbled on by chance. It's a bit southern-England-centric so please add any you've found!
Information correct at time of going to press, use at your own risk, etc.
The Hovercraft Museum, Lee-on-Solent:
Hovercraft from DAD
Old Buckenham Airfield, Norfolk:
Tank from GE (displayed at the gate)
National Motor Museum, Beaulieu, New Forest:
Bentley 4.5 Litre Supercharged, as owned by Bond in the novels
Chitty Chitty Bang Bang
Corgi model Bond cars
(NB: Beaulieu was the home of Bond in Motion before it went to London)
Royal Armouries, Leeds:
Display case of gun types used in the novels and films
St Margaret's Museum, St Margarets-at-Cliffe, nr Dover:
Small display about Ian Fleming (who had a holiday home here) and Noel Coward (who sold it to him)
Wings Museum, Balcombe, Sussex:
Douglas DC-3 cockpit used in Quantum of Solace
Shuttleworth Collection, Bedfordshire:
Little Nellie (the one flown by Ken Wallis; the version at Bond in Motion is the one Sean Connery sat in)
The Historic Dockyard, Chatham, Kent:
Model sub from TND (the Ropewalk also appears in the Thames boat chase scene)
Luchtvaartmuseum Aviodrome, Lelystad, Netherlands:
Beechcraft Twin Beech from OP
Not a museeum but the Back Factory (which is a german fastfood chain), right next to Checkpoint Charlie in Berlin has the Mini Jet from OP on Display, plus some pictures from the shoot of OP.
Is there anything Bond-related to see at the British Motor Museum (Coventry/Warwick)? I'll be heading there soon.
And what about the Aston Martin factory next door? Do they have a museum or do they offer a tour?
I'm afraid I can't tell you about the factory either. There's an Aston museum in Oxfordshire but it's pretty small, I think; I happened to pass a sign for it and looked it up when I got home: https://www.amht.org.uk/the-museum
Some years ago, I and some classmates ate there when we were on a class trip to Berlin. Didn't know about the OP memorabilia they have on display beforehand, so it was a very cool surprise!