Paddington/Bayswater would probably mean its easier to get out towards the west of London, White Waltham, Booker, Denham and maybe Elstree. Thats not a part of the world I know well I'm afraid.
If its raining, then I suggest a trip to RAF Museum at Hendon in north London, or further afield to the Imperial War Museum at Duxford which is near Cambridge.
But keep us posted & I'm sure someone will oblige.