Bulk gold has a very characteristic warm yellow shine to it, whereas almost all other metals have a grey or silvery color. Where does this come from?

I have heard that this property arises from relativistic effects, and I assume that it has to do with some distinct electronic transition energies in the gold atoms. But what changes with the "introduction" of relativistic effects, that then changes the energy of the frontier orbitals in such a drastic manner?

Yes, this is a beautiful question.

As you said, in lower rows of the periodic table, there are relativistic effects for the electrons. That is, for core electrons in gold, the electrons are traveling at a significant fraction of the speed of light (e.g., ~58% for $\ce{Au}$ $\mathrm{1s}$ electrons). This contracts the Bohr radius of the $\mathrm{1s}$ electrons by ~22%. Source: Wikipedia

This also contracts the size of other orbitals, including the $\mathrm{6s}$.

The absorption you see is a $\mathrm{5d \rightarrow 6s}$ transition. For the silver $\mathrm{4d \rightarrow 5s}$ transition, the absorption is in the UV region, but the contraction gives gold a blue absorption (i.e. less blue is reflected). Our eyes thus see a yellow color reflected.

There's a very readable article by Pekka Pyykkö and Jean Paul Desclaux that goes into more detail (if you subscribe to ACS Acc. Chem.Res.)
