What prevents bosons from occupying the same location?

Er ... nothing prevents this. That's what a Bose-Einstein condensate is: lots of bosons in the same place and quantum state.

You are observing that the state is not perfectly localized, but that is a consequence of the state not being exactly zero momentum. Ultimately the Heisenberg principle puts a lower limit on how localized they could be.

If the bosons are composite objects (like Helium atoms, say) then you can write the state in terms of their constituent parts and the Fermionic bits have to obey the Pauli principle.

This is really just a comment to dmckee's answer, but it got a bit long for a comment.

The problem with your question:

what keeps bosons from occupying the same location?

is that no particle has a precisely defined position. Remember that when we get down to the sizes of atoms etc particles don't have a position. They are described by a wavefunction that may be localised in space to some extent but never localised down to a single point. As dmckee says, the Heisenberg Uncertainty Principle prevents a particle from being localised down to a point, unless that is you're prepared to allow the momentum to become infinitely uncertain in which case the whole thing turns into a black hole!

In a BEC all the atoms are in the same quantum state, but that state is only localised down to the size of the experimental apparatus. In principle you could make the size of the condensate smaller, but I suspect the increased uncertainty in the momentum would make it hard to keep the condensate coherent and it would break up into individual atoms of different energies.