You'll end up on the beach. Elizabeth will move ahead and you'll soon lose her from your line of sight. You don't have to be too hasty about finding her and as a result it's a good idea to explore the beach in order to find plenty of silver eagles, food and drinks. The most important item is hidden beneath the trailer with painted stripes - it's a Voxophone #17: Born in the River - Ed Gaines.
Once you've explored the first beach head to the corridor leading to the next one. The corridor itself contains a Vantage Point #12: Kinetoscope - Battleship Bay. Before entering the second beach you should also check a maintenance room. There are supplies and money there.
Just as before, you don't have to be too quick about finding the girl. Elizabeth is dancing on the pier and you should make sure to explore the beach before approaching her. Get to Elizabeth once you're ready to move on with the mission.