Once you cross over to Brooklyn via the Brooklyn Bridge, there are quite a few famous places to eat.
First there is the amazing (amazingly long queue too) pizza shop known as Grimaldi Pizza. You have to try it. It is very good !
Here’s instructions from Grimaldi to Brooklyn Bridge which I then use in opposite direction to get from Brooklyn Bridge to Grimaldi :)
HOW TO GET TO THE BROOKLYN BRIDGE WALKWAY FROM GRIMALDI’S:
Do not cross Old Fulton Street yet, but instead stay on the same side of Old Fulton as that where you find Grimaldi’s and the River Café. Turn left, and walk up Old Fulton Street. You will cross Front Street, and will parallel the stone structure of the anchorage of the Brooklyn Bridge. Pass under the elevated highway and continue forward along Old Fulton Street until you come to Prospect Street. Turn left on Prospect Street and pass under the Brooklyn Bridge structure to Washington Street/Cadman Plaza East. Turn right and cross Prospect Street. A little way ahead of you, on the right side, is a stone wall. In that stone wall is the entrance to a staircase. That staircase will take you up to the walkway of the Brooklyn Bridge.
A stone throw away, there is the Brooklyn Ice Cream Factory
And if you are feeling rich (and romantic), there is the world famous River Cafe by the bayside too
And finally, after all is done, walk to the bay side for a wonderful view of New York City from Brooklyn.
Just dun be idle :)