Compared to the gravitational fields galaxies orbiting other galaxies deal with Mercury orbiting the Sun is extreme. So are GPS satellites orbiting Earth.
Mass of Sun: Ms = 1.99e30 kg
Distance to Mercury from Sun: Rm = 5.83e10 m
Mass of Milky Way galaxy: Mg = 6e42 kg
Q: At what distance R from the Milky Way would something have to be to experience the same gravitational field strength from the Milky Way that Mercury feels from the Sun?
A: We want R such that Ms/Rm^2 = Mg/R^2 or R = Rm sqrt(Mg/Ms) = 1.0e17 m.
Let's convert that to lightyears. There are 9.46e15 m/ly. The final result is 10.75 ly. Note that everyplace that close to the center of mass of the Milky Way is inside the galaxy. Anything actually outside the galaxy would be at least 5000 ly away and feel a gravity field at most 1/200000th as strong as what Mercury feels.
For Earth use the same calculation from above but replace Mg with the mass of the Earth, 5.97e24 kg. That gives that the distance from Earth where something would feel the same field strength from Earth that Mercury feels from the Sun is 1.0e9 m. That's a little over 4x the radius of the orbits of GPS satellites, so GPS satellites are feeling a little under 16x the field strength from Earth that Mercury feels from the Sun.