The parent of the Quadrantid meteor shower is the inactive solar system small body (196256) 2003 EH1. EH1 has likely only gone dormant in the past few hundred years, and may be related to the bright comet C/1490 Y1. Compared with the other best-studied inactive meteor shower parent (3200) Phaethon, EH1 has received comparatively minimal characterization of its surface properties. We present the first reflectance spectrum and additional photometry of EH1, as well as new spectra of the nuclei of three nearly dormant comets P/2006 HR30 (Siding Spring), 364P/Pan-STARRS, and 249P/LINEAR for comparison. We also present new short-term high-resolution orbital integrations of these bodies for context. EH1s spectrum is red in color below 0.8 μm in between C and D types, consistent with previous photometric measurements, but is blue beyond 0.8 μm until at least 1.02 μm. 249P and 364P have both red slopes consistent with C taxonomic types and HR30 has a classic comet nucleus D-type slope. If the downturn in EH1's spectrum is due to an absorption feature, magnetite and olivine are plausible candidates, but more data are needed. 249P and 364P have similar recent and historical dynamical evolutions in addition to their similar surface properties. We discuss the interrelation between the dynamical histories and modern surfaces of these four objects and suggest avenues for further study to better constrain how the Quadrantids and Geminids were created.