As for the remaining states:
NY: As I said, probably Oyster Bay town. Only NYC, Hempstead, Brookhaven, and Islip are larger. NYC and Hempstead are solidly Democratic. Brookhaven and Islip both voted about 53% for Obama in 2008, and Suffolk County had only a very small swing toward Romney in 2012. Thus, it is very likely that both Brookhaven and Islip also voted for Obama in 2012, which leaves Oyster Bay town as the answer.
OR: Medford voted for McCain, and Jackson County swung toward Romney, so it almost definitely voted for Romney. As for larger cities, there are only 7: Portland, Salem, Eugene, Gresham, Hillsboro, Beaverton, and Bend. Portland, Eugene, Hillsboro, and Beaverton are all solidly Democratic. Gresham almost definitely voted for Obama in 2012 since it voted 58% for Obama in 2008 and Multnomah County had only a very small swing toward Romney. Salem voted 56% for Obama in 2008, and is getting more Hispanic - hardly a recipe for larger Republican vote shares. Bend also voted 56% for Obama, and Deschutes County swung only about 2% toward Romney, so it probably voted for Obama in 2012 as well. That leaves Medford as the very likely answer.
AL: Probably Hoover, but I don't have any solid evidence to back that up.
DE and WV: I have no clue.
I'm not sure if I would consider the town governments on Long Island as cities, (the towns themselves are made up of a bunch of communities, some of which are villages, which have their own local government as well). With that being said using that definition Oyster Bay would be the answer, Obama received 51% in Brookhaven and 54% in Islip.
