It takes a while to get out to Coney Island by subway – about 40 minutes from Downtown Brooklyn and at least an hour from midtown Manhattan – so plan to have a day trip, preferably in spring or summer when the weather's nice and the amusement parks are open for the season (daily from Memorial Day through Labor Day; weekends only in April, May, September and October). The beach and boardwalk are open year-round, though lifeguards don't patrol out of season.
In high season, aim to get there by noon so you can hit up Luna Park and try the rides before it gets too crowded. After you've had your fill of thrills, grab a couple of Nathan's Famous hot dogs, then spend some time on the beach and the boardwalk, dipping your toes in the Atlantic when you start feeling the heat. If you prefer a bit more international flair, walk a mile east along the boardwalk for some Russian food in Brighton Beach. Spend some time browsing the shops along Brighton Beach Ave and hop either the subway or bus back to Stillwell Ave for some authentic old-time pizza at Totonno's.
Cap it off with an evening game of minor-league baseball to cheer on the Brooklyn Cyclones (especially if they're playing crosstown rivals the Staten Island Yankees), or else just relax with some beer on the boardwalk at Ruby's and watch the sun go down. If you're there on a Friday night in July or August, stick around for the fireworks show at 9:30pm.