Thanks @Ric and @peekay123. Found another post about the INPUT:
I did check the document and it looks like all pins except A3 and DAC are 5V tolerant (when not in analog mode).
I then tried switching from INPUT to INPUT_PULLDOWN (and INPUT_PULLUP for good measure). I still get the floating between HIGH/LOW with nothing connected.
Even when I connected a cable from A5 to D4 it still continues to float. D1 however, does seem to stay in a state with INPUT_PULLDOWN. Unattached or attached to GND, it stays LOW. Connected to A5, it goes HIGH. It takes a while to test each pin and let it cycle through several times, but D1 seems reliable while D2-D5 do not (they float between states).