Euclid is poised to make significant advances in the study of nearby galaxies in the Local Universe. Here we present a first look at six galaxies observed for the Nearby Galaxy Showcase as part of the Euclid Early Release Observations acquired between August and November, 2023. These targets, three dwarf galaxies (Holmberg II, IC 10, and NGC 6822) and three spirals (IC 342, NGC 2403, and NGC 6744), range in distance from about 0.5 Mpc to 8.8 Mpc. We first assess the surface brightness depths in the stacked Euclid images, and confirm previous estimates in 100 arcsec2 regions for Visible Camera (VIS) of 1σ limits of 30.5 mag arcsec-2, but find deeper than previous estimates for Near-Infrared Spectrometer and Photometer (NISP) with 1σ = 29.2-29.4mag arcsec-2. By combining Euclid HE, YE, and IE into RGB images, we illustrate the large field of view (FoV) covered by a single reference observing sequence (ROS), together with exquisite detail on scales of <1-4 parsecs in these nearby galaxies. Our analysis of radial surface brightness and color profiles demonstrates that the photometric calibration of Euclid is consistent with what is expected for galaxy colors according to stellar synthesis models. We perform standard source-selection techniques for stellar photometry, and find approximately 1.3 million stars across the six galaxy fields. After subtracting foreground stars and background galaxies, and applying a color and magnitude selection, we extract stellar populations of different ages for the six galaxies. The resolved stellar photometry obtained with Euclid allows us to constrain the star-formation histories of these galaxies, which we do by disentangling the distributions of young stars and asymptotic giant branch and red giant branch stellar populations. We finally examine two galaxies individually for surrounding systems of dwarf galaxy satellites and globular cluster populations. Our analysis of the ensemble of dwarf satellites around NGC 6744 recovers all the previously known dwarf satellites within the Euclid FoV, and also confirms the satellite nature of a previously identified candidate, dw1909m6341, a nucleated dwarf spheroidal at the end of a spiral arm. Our new census of the globular clusters around NGC 2403 yields nine new star-cluster candidates, eight of which exhibit colors indicative of evolved stellar populations. In summary, our first investigation of six "showcase" galaxies demonstrates that Euclid is a powerful probe of stellar structure and stellar populations in nearby galaxies, and will provide vastly improved statistics on dwarf satellite systems and extragalactic globular clusters in the local Universe, among many other exciting results. ★This paper is published on behalf of the Euclid Consortium.