We introduce the Solitary Local dwarfs survey (Solo), a wide-field photometric study targeting every isolated dwarf galaxy within 3 Mpc of the Milky Way. Solo is based on (u)gi multiband imaging from Canada-France-Hawaii Telescope/MegaCam for northern targets, and Magellan/Megacam for southern targets. All galaxies fainter than MV ≃ -18 situated beyond the nominal virial radius of the Milky Way and M31 (≳300 kpc) are included in this volume-limited sample, for a total of 42 targets. In addition to reviewing the survey goals and strategy, we present results for the Sagittarius dwarf irregular galaxy (Sag DIG), one of the most isolated, low-mass galaxies, located at the edge of the Local Group. We analyse its resolved stellar populations and their spatial distributions. We provide updated estimates of its central surface brightness and integrated luminosity, and trace its surface brightness profile to a level fainter than 30 mag arcsec-2. Sag DIG is well described by a highly elliptical (disc-like) system following a single component Sérsic model. However, a low-level distortion is present at the outer edges of the galaxy that, were Sag DIG not so isolated, would likely be attributed to some kind of previous tidal interaction. Further, we find evidence of an extremely low level, extended distribution of stars beyond ˜5 arcmin (>1.5 kpc) that suggests Sag DIG may be embedded in a very low-density stellar halo. We compare the stellar and H I structures of Sag DIG, and discuss results for this galaxy in relation to other isolated, dwarf irregular galaxies in the Local Group.