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Context. Nearby open clusters, such as Pleiades, Praesepe, and Blanco 1, have been extensively studied due to their proximity to the Sun. The Gaia data provide the opportunity to investigate these clusters, because they contain valuable astrometric and photometric information that can be used to update their kinematic and stellar properties. Aims. Our goal is to carry out a star membership study in these nearby open clusters by employing an astrometric model with proper motions (PMs) and an unsupervised clustering machine learning algorithm that uses positions, PMs, and parallaxes. The star members are selected from the cross-matching between both methods. Once we know the members, we investigate the spatial distributions of these clusters and estimate their distances, ages, and metallicities. Methods. We used the Gaia DR3 catalogue to determine star members using two approaches: a classical Bayesian model and the unsupervised machine learning algorithm DBSCAN. For star members, we built radial density profiles and spatial distributions, and computed the King parameters. The ages and metallicities were estimated using the BASE-9 Bayesian software. Results. We identified 958, 744, and 488 star members for Pleiades, Praesepe, and Blanco 1, respectively. We corrected the distances and built the spatial distributions, finding that Praesepe and Blanco 1 have elongated shape structures. The distances, ages, and metallicities obtained were consistent with those reported in the literature. Conclusions. We obtained catalogues of star members, and updated kinematic and stellar parameters for these open clusters. We find that the PMs model can find a similar number of members to the unsupervised clustering algorithm when the cluster population forms an overdensity in the vector point diagram. This allows us to select an adequate size of the PMs region with which to run these methods. Our analysis found stars that are being directed towards the outskirts of Praesepe and Blanco 1, which exhibit elongated shapes. These stars have high membership probabilities and similar PMs to those within the tidal radius