The ferries at Eminonu are the cheapest good thing in Istanbul. For the price of a metro ticket you cross between two continents on the deck of a working commuter boat, with the old city receding behind you.
Lines run to Kadikoy and Uskudar every twenty minutes or so, and longer routes go up the Bosphorus towards the Black Sea. Late afternoon is the hour to go: the light turns gold on the water and the domes behind you catch it.
Tea is served on board, and feeding simit to the gulls is a local habit rather than a tourist one. From Romance Istanbul Hotel the pier is around ten minutes on foot, downhill all the way.