Deep within the Old Woods, farther in than most hunting parties dare to tread, a short, stone tower juts forth from the landscape. To an observer, there is a certain strangeness about it, as if the pattern the windows are in is somehow wrong. There are no doors, and all of the windows are barred shut but for a single small window near the base of the tower, just large enough for a man to crawl through.
About a yard from this window a wooden signpost has been driven deep into the ground. It has a single word painted on it: NON. Careful observers will find that the paint used to write the word appears to have dripped up the sign in minute portions. If the sign is significantly disturbed, it will come loose from the ground and hurtle inexplicably upwards into the heavens.
Inside the Tower
If the tower is entered through the small open window, one will find that the inside of the tower is much like one would expect the inside of a tower to be - it's divided up into furnished rooms, with doors and stairs. There is one bit of strangeness - anyone who enters the tower will find that the entire inside is arranged as if upside-down. Doors extend downwards from the ceiling, stairs are carved into the ceiling. Furniture sits easily upon the ceiling, not bolted or fastened down but merely resting there 'normally.' Naturally, this makes movement through the tower a more difficult than normal endeavor, if not a terribly dangerous one.
Anything found in the tower seems totally normal except for a single inexplicable property - it all falls upwards, as if propelled away from the earth. Even if removed from the tower it retains this property.
There are only a few things in the tower which behave normally - a few rocks, sticks, and a single deer carcass, slain with an arrow.
Inhabitants of the Tower
Eventually, intruders will meet the inhabitants of the Tower of NON. There are only a small handful of people living in the tower, and they, like everything else found in the tower, move around on the ceiling and fall upward. The windows have obviously been barred shut for their safety, to keep them from falling up into the bottomless heavens. In appearance, they look normal.
Fortunately, the people here are friendly. They will happily reveal that they are a team of explorers and scientists, come from the other side of the world to see what life is like on this side. Obviously, this is why they, and their possessions, fall upwards - gravity works opposite on them. Otherwise, they would of course fall off the world, living on the bottom of it as they do!
Because this trait makes outside exploration so dangerous for them, the people here have unfortunately accomplished depressingly little in their stay thus far. They are thrilled to have visitors to speak with, ask questions of, and potentially buy things from. While they have relatively little in the way of conventional valuables, obviously anything which falls upwards has a degree of value in and of itself!
At the bottom of the tower is a cellar, and from it tunnels delve deep into the earth. It's from these tunnels that the stone was cut to make the tower (if it used upwards-falling stone, it would be too unstable to live in!). In addition, traveling through these tunnels will eventually take one to the other side of the world, though any erstwhile explorers will find there similar troubles to the ones had here by the people of the tower.
This is another one to see 'because it's there,' but there are lots of things that could come of it, too. Exchange of extremely different cultures. Quests to find objects for the people of NON. Adventure to the other side of the world!
Alternatively, you could have less peaceful people in the tower - while an invasion is very unlikely to be successful (imagine the logistical struggles alone!), you could run a nifty fight scene involving people on the floor fighting people on the ceiling, with the possibility of hurling people out the window to plunge screaming into the upper atmosphere.
A final note: Why NON? Because NON reads the same way both right side-up and upside-down.
Additional Ideas (1)
A sword or other weapon weighing nothing but still possessing the mass a proper weapon needs.
A sturdy pack which cancels the weight of items placed within.
A perfectly balanced arrow which fires further because gravity doesn't pull at it as strongly,
Heavy iron boots which make the wearer lighter on his feet.