Background: Elastic electron scattering has been used for decades to paint the most accurate picture of the proton distribution in atomic nuclei. This stands in stark contrast to the neutron distribution that is traditionally probed using hadronic reactions that are hindered by large uncertainties in the reaction mechanism. Spurred by new experimental developments, it is now possible to gain valuable insights into the neutron distribution using exclusively electroweak probes.Purpose: To assess the information content and complementarity of the following three electroweak experiments in constraining the neutron distribution of atomic nuclei: (a) parity violating elastic electron scattering, (b) coherent elastic neutrino nucleus scattering, and (c) elastic electron scattering of unstable nuclei. Methods: Relativistic mean-field models informed by the properties of finite nuclei and neutron stars are used to compute ground state densities and form factors of a variety of nuclei. All the models follow the same fitting protocol, except for the assumed-and presently unknown-value of the neutron skin thickness of 208 Pb. This enables one to tune the density dependence of the symmetry energy without compromising the success in reproducing well known physical observables. Results: We found that the ongoing PREX-II and upcoming CREX campaigns at Jefferson Lab will play a vital role in constraining the weak form factor of xenon and argon, liquid noble gases that are used for the detection of both neutrinos and dark matter particles. Conclusions: Remarkable new advances in experimental physics have opened a new window into ground state densities of atomic nuclei using solely electroweak probes. The diversity and versatility of these experiments reveal powerful correlations that impose important nuclear structure constraints. In turn, these constraints provide quantitative theoretical uncertainties that are instrumental in searches for new physics and insights into the behavior of dense matter.