Today, our highest-resolution gravitational maps of the Earth are from the Gravity Recovery and Climate Experiment (GRACE) project, launched in 2002.
That's not the case. The latest GRACE gravity model, which combines results from the GRACE and GOCE gravity missions and DTU13 is a 360x360 (degree and order) gravity model. On the other hand, the EGM2008 model "is complete to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159." How much of that is pure fiction is a matter of debate.
An alternative is to combine satellite-based observations with terrain. The images below depicts radial gravity anomalies over a 400x400 km area about Mount Everest (circled). The spatial resolution of a satellite-only model based on combined GRACE and GOCE data is about 100 km. Adding EGM2008 improves the resolution to about 10 km. Incorporating terrain knowledge improves the resolution even further, to about 200 meters.
Combining satellite-based gravity experiments with terrestrial observations has pluses and minuses. On the plus side, satellite-based observations are rather coarse but are global in nature, while terrestrial-based observations can be extremely fine but are local in nature. On the minus side, satellite-based observations are sensitive to the mass of the atmosphere while surface-based observations are not, and satellite-based and surface-based observations measure different things. There's always a potential for injected errors when combining measurements different things.