If we live in the vicinity of the hypothesized Great Attractor, the age of the universe as inferred from the local expansion rate can be off by 3 per cent. We study the effect that living inside or near a massive overdensity has on cosmological parameters induced from observations of supernovae, the Hubble parameter and the cosmic microwave background. We compare the results to those for an observer in a perfectly homogeneous Λ cold dark matter universe. We find that for instance the inferred value for the global Hubble parameter changes by around three per cent if we happen to live inside a massive overdensity such as the hypothesized Great Attractor. Taking into account the effect of such structures on our perception of the universe makes cosmology perhaps less precise, but more accurate.