Gravity thought experiments

For some reason (probably reading my son "The Magic School Bus Lost in the Solar System"), I started wondering about gravity. I was wondering why my sensation of gravity is just being pulled down, and not to the sides as well. I guess the mass to either side of me in the Earth is roughly equal and thus cancels itself out. Which made me wonder how something would fall if you happened to be standing on the edge of a hemisphere, or if there was a cylindrical space running through the center of the Earth. In the later case I would have thought that something might fall down past the Earth's center overshoot, and them fall back, oscillating until it eventually came to rest a the center. Not sure about the hemisphere example. Seems like something dropped might actually fall diagonally. Of course the natural rest state of objects large enough to have noticeable gravity is a sphere, so such toroidal or hemispherical objects would not occur without some kind of intervention. The funny thing about gravity is that all matter attracts other matter. I don't notice being sucked towards the computer because it has so little mass, but the mass of the Earth is huge and sucks me towards it. I wonder if there are objects in the universe massive enough for gravity to be noticed, but in different shapes so that the force of gravity is felt in directions other than straight down ...?