If you started going up in the air from where you are now, you would eventually leave the atmosphere and enter Space. You would leave the Solar System, and then enter Deep Space. You would see other stars, nebulae, galaxies, red dwarfs, supernovae, and black holes. If you reached the edge of the Universe, you would would start travelling along the surface of expanding Space-Time.
Space-time is ever-so-slightly curved ensuring anybody can move faster than the speed of light only by flying in circles right back to where they began. Sort of like a song that gets stuck in your head and drives you nuts or Einstein's rubber sheets which suggest some things cannot be unseen including naked singularities with all their lotions in motions rubbing up against space-time in the most intimate ways.
Nobody ever lost money underestimating the average intelligence of the American public who know the meaning of null, void, and vacuous quite intimately from birth allowing them to boldly go where none has gone before only to have people regret that they somehow came back. Americans were the first space-cadets right after the Russians and the chimps having found fame and glory exploring empty space in between their ears first and later in orbit high as a kite.
I would traverse right into a black hole if i could fly through space. I believe that a black hole is simply nothing more than the opposite end of a white hole, a hole in which matter is thrown out into another universe. So hopefully I'd eventually find a really cool universe. You loser can have this one, lol.
If you keep on travelling , would you reach an another universe ! Some physicists say it is a multiverse out there complete with parallel universes or alternative universes.
This is true only if the universe has a positive curvature. If the universe is flat or has a negative curvature then it is infinite in extend, meaning you would just keep on traveling forever.