Taksim square, walk down the istiklal avenue, see galata tower and walk down to karaköy, take the tram to sultanahmet if you are into history, take a bus towards the opposite direction if you want a more modern experience and go to bebek. From either places cross the bridge, to Anatolian side.
Also check out this posting for more ideas: Could you suggest a basic 1-day itinerary for Istanbul?
