You are correct that energy cannot be created nor destroyed, but you're missing the second and crucial part of that saying: energy can only be transferred from one place or form to another. Another important point is that potential energy is a relative term that must be defined in terms of the system you are studying.
Your object on the floor has zero potential energy, with respect to the floor, and it didn't destroy any energy to get there. As it fell or was placed on the floor it simply converted gravitational potential energy into air movement, sound, and heating of the floor (and movement of the floor, depending on how heavy the object is).
If you expand your system to include the world outside the room, then the object and everything in the room still have gravitational potential energy with respect to other "zero points" (the floor of the basement below, the bottom of the hill outside, etc.). Expanding even more, everything on earth has gravitational potential energy with respect to the Sun, and everything in our Solar System has gravitational potential energy with respect to the rest of the universe. As far as everyday applications go however, it is usually sufficient to stop at the floor...