I would avoid all the places you list, none of them are going to be particularly good (unless you love raw seafood, in which case you can get yourself an enjoyable meal at Old Ebbitt), and I don't think they will feel as special as you hope. Note that the Hamilton isn't even old or classic.

If you want to try DC restaurants that are local institutions and also actually have good food, maybe try Iron Gate, Tabard Inn for brunch, 1789 in Georgetown, Le Diplomate, or Rasika.