I really like this paper for this topic:
As the title says it is “A semiquantitative treatment of surface charges in DC circuits” (Rainer Mueller).
Surface charges accumulate wherever there is a sudden change in the direction of the electric field lines from inside the wire to outside. Overall, you tend to get positive charge accumulating near the positive terminal and negative charges accumulating near the negative terminal, and you have both positive and negative charges accumulate on opposite sides of the wire near bends.
Unfortunately, there is no one simple overall statement about the distribution. The charge distribution depends strongly on the geometry of the circuit layout. Circuit theory neglects the geometry of the circuit layout. So you need to use Maxwell’s equations which depend on the geometry.