When looking at high-quality models of human heads, I often see a neat pattern of quads, arranged around the eyes and mouth. Is there a tool (within Houdini or otherwise) which can take a "messy" triangular mesh and convert it into such high-quality, neatly arranged quads?

The Labs toolset has a Quadrangulate node that attempts to quadrify triangulated meshes. There is also Exoside's Quadremesher node, but to use it you need a separate (non-Houdini) paid license. Your mileage may vary with either method, although Quadremesher seems to produce decent results.

Thanks, I'll look into these.

Labs also has Instant Meshes, which is open source quad remesher, should be also able to take curves as a second input to further enforce some flow