The best champs outside of lane to counter Draven include Naafiri, Karthus, and Xin Zhao. These champs are all good at countering Draven with decent win rates over 59%. Even if these Draven counter picks are not used in the same position as you, it's not smart to take him into these matchups. They will usually win against Draven.
Yet, if the opposing team brings either Maokai or Rumble, you should strongly consider taking him, as he easily beats these champs with win rates over 55% against each ofthem.