Where do objects go when they enter a black hole?
We can't be sure what happens when an object falls into a black hole as our physics can't describe it.
First of all what we mean by the surface of a black hole is its event horizon. This is the point surface where an external observer can't see or communicate in any way with an object inside the event horizon.
To an external observer any object never passes the event horizon. To an observer passing through the event horizon, assuming they can survive the gravitational tidal forces, wouldn't see that they had crossed the event horizon.
The main problem is that our understanding of the physics of black holes doesn't work. There are two major issues.
General Relativity predicts a singularity inside the black hole into which all things must ultimately fall. The singularity can't be described by any physics we know and needs new theories to explain it.
There is also the information paradox. When something falls into a black hole its information can't be lost. Stephen Hawking has a theory that the information is somehow stored in the event horizon which may explain it.