I have a vivid memory of seeing the premier of 2001 A Space Odyssey in
1968.  At the time, I was only six years old, but I vividly recall a
scene in which a young women in must have been go-go boots, walks
upside down to tune of Nancy Sinatra's, 'These Boots are Made for
Walkin" -- the same song that Kubrick deployed in a different context
in Full Metal Jacket. Does anyone else recall the scene? And might it
be one that was removed when Kubrick reduced the film by 19 minutes? 
If you know, then please let me know.

Thanks,

I own six slightly different versions of the movie (I understand there
may be as many as thirty, including the 1976 TV version and the 1980
and the 25th anniversary theatrical releases) and none I have seen
have the music you describe. There is the scene with the stewardess
walking upside down-- in a manner of speaking-- but the music is
classical.

Could you have seen a parody?

I must admit that I only remember the stewardess walking around the
ship to the music of the Blue Danube. The music, Boots are Made for
Walkin, would utterly clash with the remaining soundtracks.
http://i.cnn.net/v5cache/TCM/Images/Dynamic/i31/2001SpaceOdyssey_FF_300x225_050220051550.gif

Starting on the day of the film's premiere, I must have seen "2001: A
Space Odyssey" at least a hundred times, in every version available to
me. I have never seen a version that used "These Boots Are Made for
Walkin'" in the scene with the inverted stewardess.

Memory can play tricks on us.

I have "only" seen "2001" a couple of dozen times, including the first run,
and nope, no "These Boots ..." scene is in the movie.

Looking Forward, denco-ga - Google Answers Researcher

Perhaps the scene that you recall was from an advertisement that
screened with the movie?

I also saw 2001 in 1968 (when I was ten). I also have a vague memory
of a "go-go chick" walking upside-down to "These Boots Are Made For
Walkin'" - but my memory of that is not associated with 2001.

Like the other commenters , I remember the stewardess walking upside
down to the music of the Blue Danube but certainly not "These Boots
were made for walking".

I will always consider this by far my favorite film. I have  seen it
perhaps a dozen times (so I have a long way to go before I break
Pink's Record)

I remember my first time seeing it which was at the Odeon Cinema in Belfast.
I saw it with various members of my family on the same evening
Armstrong, Aldrin and Collins had just returned from the moon. At the
end of the movie
my brother and cousin exclaimed with some indignation "What was that
all about?" (As I had dragged them along they must have felt it was an
evening wasted)

When I saw the film a second time (this in the more luxurious
surroundings of the Empire theatre in Leicester Square) I discovered
to my horror that key sequences had been cut from the Belfast viewing
(including scenes from the David Bowman's confrontation with HAL and
the "Star Gate Sequence")

I guess that the Belfast film censors / editors figured that most
normal Northern Irish people could only sit through a reduced version
of this highly simulating movie. :-)

Mongolia