The observed flattening of rotation curves is usually considered strong evidence for the existence of dark matter on galactic scales. However, observations such as the Baryonic Tully-Fisher Relation and the Radial Acceleration Relation suggest that the observed dynamics in galaxies are strongly correlated with the distribution of baryonic matter. This is challenging to explain in the context of dark matter, motivating low-acceleration modifications to gravity as an alternative to the dark matter hypothesis. I will present a framework to test a general class of modifications to gravity using local Milky Way observables that probe both the radial and vertical components of the galactic acceleration. For concreteness, I will focus on Modified Newtonian Dynamics (MOND), a modification to gravity that increases the magnitude but does not change the direction of the gravitational acceleration. I will show that a modification to gravity of this type is in tension with observations of the Milky Way's baryonic profile and that a spherical dark matter halo provides a better fit to the data. I may also discuss current work extending this analysis to other theories such superfluid dark matter.