Think of it this way... I probably would not be allowed to ride a unicycle down the sidewalk of a city that doesn't allow bicycles on the sidewalk. I would be forced to ride my unicycle in the road. Obviously, I wouldn't ride the unicycle in the road, injury would be certain. Therefore, I can't use my unicycle for transportation. The legislators would say too bad, we're keeping the pedestrians safe.
It depends on the the law, but more than that it depends on the interpretation of the law by its enforcers. Many unicyclists have trouble with this: some have been told by a policeman to get of the sidewalk, and one block later have been told to get off the road. Part of it depends on speed- if you are on a coker, you will probably average about 12 mph, the top speed of the segway. Needless to say, a unicycle with a 36" wheel is probably a bit more visible than a segway. A coker is generally considered a road machine, as the gyroscopic stabilization begins to take effect at cruising speed. As you go down in wheel size or up in crank size, your speed is reduced. Your standard unicycle, the 20" or 24", are generally used on sidewalks; their smaller wheel size allows for maneuverability and street tricks, if you feel so inclined. 29ers are somewhat ambiguous, depending on the crank length.
However, if riding on the sidewalk is declared off limits by law, most unicyclists will take to the road, or go down to city hall and request separation of bicycle and unicycle definitions. Most of the time though, as a unicyclist you have just as much right to the sidewalk as the street- it is a gray area, and common sense is what dictates your choice of sidewalk or street. Riding on a street isn't always safe, but neither is riding on the sidewalk.
The best solution to all the segway problems? If you're considering getting a segway, save yourself a few thousand dollars and buy a unicycle instead.