Do electrons go towards higher voltage or lower voltage?
I feel like Thomas Edison really screwed me when he made everyone believe that current is movement of positive charges.

As we're 'clearing things up', let's be very careful in our language.
Current is the movement of charges, both negative and positive.
Current, aka Conventional Current (because its direction is subject to a convention), is defined to flow in the direction the positive charges are moving, and opposite to the direction the negative charges are moving.
In any given medium, there may be several species of particle that carry charge, and are able to move, and so can give rise to a current.
In water, the OH- and H3O+ ions are able to move.
In ice however, only the H+ can move.
In copper sulphate solution, [Cu(H2O)6]2+ and SO42- are mobile
In semiconductors, the holes1, and some of the electrons, are able to move
In metals, some of the electrons are free to move.
In a fully developed plasma, all of the electrons, and the bare nuclei, are free to move.
When you do a mesh analysis of a circuit, you label the mesh with current direction arrows. This can be done arbitrarily, and the solution will tell you whether the currents are negative or positive. In any non-trivial mesh, you will have to add and subtract currents, and this would be true regardless of the convention you use for the direction of conventional current.

Do electrons go from high voltage to low voltage or from low voltage to high voltage?

If by 'high voltage' you mean 'more positive voltage', then a mobile electron would tend to move to a high voltage electrode, as would all other negative charge carriers. Mobile positive charge carriers move to the less positive electrode. So for instance in copper sulphate electrolysis, the copper anode dissolves, as the copper ions move across to the cathode.

1 A hole is just as much of a quantum mechanical particle as an electron, it has mass, velocity, momentum, charge. I'm not saying it is a particle, just if that you model an electron as a particle for conduction purposes, then the same model fits a hole.