Would you expect that anions would be physically closer to the oxygen or to the hydrogens of water molecules that surround it in solution?

Anions are negatively charged particles. The water molecule is a polar molecule, that means that, it is partly positive and partly negative. The oxygen atoms in the water molecules are more electronegative more than the hydrogen atoms and they draw the shared electron nearer to themselves than the hydrogen atoms; this make them to be slightly negatively charged while the hydrogen atom is slightly positively charged.
Therefore in solution, the anions would be attracted toward the hydrogen atom that is slightly positive while the cations will be attracted to oxygen atom that is slightly negative.

False. records show otherwise