Off top of head, would suggest Sansom Street Oyster House for both. Go early--hit the bar for the shellfish specialis and cocktails. I doubt you will find whole shad--too risky for proprietor if someone chokes on a bone. It's actually getting late for shad. My, how I love it. But, I prefer an order of shad +roe--now that's eating!
Don't know where you live, but we had delicious sauteed soft shells at Yang Ming last weekend.
Sansom Street Oyster House usually has shad in season, but lately we have been enjoying the fish at McCormick & Schmick - very fresh and good, cooked perfectly - and at Estia. My husband had a whole black bass at Mc & S that was one of the best fish either of us had ever tasted. You could call and ask them what's on the menu.