Spatially-resolved spectroscopy of the environments of explosive transients carries detailed information about the physical properties of the stellar population that gave rise to the explosion, and thus the progenitor itself. Here, we present new observations of ESO184-G82, the galaxy hosting the archetype of the $γ$-ray burst/supernova connection, GRB 980425/SN 1998bw, obtained with the integral-field spectrograph MUSE at the VLT. These observations yield detailed maps of emission-line strength for various nebular lines, as well as physical parameters like dust extinction, stellar age, and oxygen abundance on spatial scales of 160 pc. The immediate environment of GRB 980425 is young (5-8 Myr) and consistent with a mildly-extinguished ($A_V∼0.1\,\mathrm{mag}$) progenitor of zero-age main-sequence mass between 25 M$_{⊙}$ and 40 M$_{⊙}$ and oxygen abundance 12+log(O/H)~8.2 ($Z∼0.3\,\mathrm{Z}_⊙$). This metallicity is slightly lower than the one of an integrated measurement of the galaxy (12+log(O/H)~8.3) and a prominent HII region (12+log(O/H)~8.4). This Wolf-Rayet region is significantly younger than the explosion site, and we argue that a scenario in which the GRB progenitor formed there and was subsequently ejected appears very unlikely. Empirical strong-line methods based on [OIII] and/or [NII] are inadequate to produce accurate maps of oxygen abundance at the level of detail of our MUSE observation as these methods over-/underestimate 12+log(O/H) at low/high ionization parameter. The metallicity gradient in ESO184-G82 is -0.06 dex kpc$^{-1}$, indicating that the typical offsets of at most few kpc for cosmological GRBs have a small impact for high-redshift measurements on average. Similarly, the GRB/SN site spectrum returns broadly comparable physical parameters to those inferred from an unresolved spectrum, which is typically obtained for high-redshift galaxies. ; Comment: 13 pages, 12 figures, submitted to A&A, version after referee comments, comments very welcome