Where is the mutual center of mass (barycenter) of the Milky Way and Andromeda located?
Answer
In the space between the Milky Way and Andromeda Galaxy
Since the two largest components are comparable in mass, the barycenter of the Local Group is located squarely in the vast expanse of space situated between the Milky Way and the Andromeda Galaxy.

Related Questions
What structural description is commonly applied to the overall shape of the Local Group?Which galaxy is identified as the largest and most massive major player within the Local Group?What is the approximate diameter span of the Local Group?What type of galaxies make up the vast majority of the confirmed membership in the Local Group?Where is the mutual center of mass (barycenter) of the Milky Way and Andromeda located?What does the barycenter being slightly closer to Andromeda imply about the mass distribution?What is the expected long-term fate for the Milky Way and Andromeda galaxies due to their current movement?At what relative velocity are the Milky Way and Andromeda currently approaching one another?Which theoretical boundary do astronomers use to define where the Local Group ends?What is the approximate mass of the third major player, the Triangulum Galaxy (M33)?What structure immediately contains the Local Group on its outskirts?