"Repair" and "repair" are two distinct words. No, really. Although they look EXACTLY alike, they draw from different wells. "Repair", as in fixing something, goes back to the Old French reparer, which stems from the Latin reparare, to restore, or put back in order. But the repair in "repair to" stems from the Old French repairer, which means to frequent, or return to. It's earlier form was repadrer, going back to the Latin repatriare, to return to one's own country.
Call me gullible, but I am not entirely satisfied by this explanation. Where did that 'i' come from in the second version? Why isn't it something along the lines of 'repatrate' to the drawing room? Doesn't it seem like their might have been just a leetle, tiny bit of blending of meanings in that "repair to", which combines both the restorative and the returning meanings of the word?
And where is Anatoly Liberman when we need him most?