RR Lyrae stars together with Cepheids are, among radial variables, the most popular distance indicators because the leading physical mechanisms which govern their pulsational instability are well known. However, the discrepancy between the distance scale based on RR Lyrae and on Cepheids has not been properly settled yet. Moreover RR Lyrae stars are also the cross-road of several long-standing problems concerning the evolutionary and the pulsation properties of low-mass stars (Bono & Stellingwerf 1994; Bono et al. 1997 and references therein). This notwithstanding only very few observational investigations have been carried out on the pulsation properties and the spatial distribution of these objects in LG galaxies (Pritchet & van den Bergh 1987). As a consequence, a systematic search of RR Lyrae variables in different components (bulge, disk, halo) of these galaxies can supply useful constraints on metallicity gradients, the morphology of field Horizontal Branch stars, the topology of the instability strip, and in turn the differences with Galactic and MC RR Lyrae stars. In this context it is worth mentioning that by relying on the current conservative estimates of the limit magnitudes in the U and the V bands of this detector at the LBT both the detection and the covering of the light curve of RR Lyrae variables could be extended to almost all north LG galaxies (Hodge 1996). This unprecedent observational effort could provide fundamental constraints on the discrepancy between the RR Lyrae and the Cepheid distance scale. The observation strategy previously outlined for classical Cepheids applies also to RR Lyrae stars.