  Optically active spin defects in solids offer promising platforms to
investigate nuclear spin clusters with high sensitivity and atomic-site
resolution. To leverage near-surface defects for molecular structure analysis
in chemical and biological contexts using nuclear magnetic resonance (NMR),
further advances in spectroscopic characterization of nuclear environments are
essential. Here, we report Fourier spectroscopy techniques to improve
localization and mapping of the testbed $^{13}\mathrm{C}$ nuclear spin
environment of individual, shallow nitrogen-vacancy centers at room
temperature. We use multidimensional spectroscopy, well-known from classical
NMR, in combination with weak measurements of single-nuclear-spin precession.
We demonstrate two examples of multidimensional NMR: (i) improved nuclear spin
localization by separate encoding of the two hyperfine components along
spectral dimensions and (ii) spectral editing of nuclear-spin pairs, including
measurement of internuclear coupling constants. Our work adds important tools
for the spectroscopic analysis of molecular structures by single-spin probes.
