Go house hunting
It's funny because, it's, like, a first date, ya know? Put search criteria in at Redfin.com that lends itself toward good first date exploring -- i.e. ocean views, secret gardens, CASTLES (!?!?!) -- and get back a map of killer open houses that probably have some free food and/or drink at them.
Enjoy the sunset
Don't tell anyone, but Casa del Mar is my favorite first date place. It’s upscale, down by the beach, has plenty of spacious seating, the drinks are good and strong, the bar food is shareable, and it’s the perfect setting for romance. While drinks and snacks will cost you as much as a nice dinner, the ambiance is worth the extra expenditure even if it doesn't work out.
Booze it up at brunch
Generally, anything that isn't an evening date is probably not a good move. But a boozy brunch is the exception. Make reservations at a brunch spot that serves bottomless (enter something alcoholic here); if you also want to get bottomless FOOD, hit A-Frame in West LA, which drops unlimited pancakes as well as mimosas.