It's amazing the change in what's important when you're on a beach vacation...As far as possessions go, all you need for all day is a suit, sandals, towel, sunscreen, a good cooler and a beach cruiser bike. 
If I had to design a beach cruiser I'd consider the following:
frame - maybe stainless steel or aluminum to resist corrosion
drivetrain - belt drive to eliminate bike chain rust.  not sure how belt drive does with sand.  single speed or sealed multiple gear hub.
brakes - coaster brakes at least or standard cantilever brakes.
tires - max traction on sand but able to ride on pavement as well.
cargo - teak lined cargo rack or baskets front and back.  Carry coolers and beach bag.  Drink holder on handlebars. 
pedals - one side of pedal for bare feet, other side with lugs for sandals or shoes.
Beach cooler design - anchor points molded into the plastic to simplify tying down to bike. 
Beach Towel Design - accommodates two, stuffs into sewn in sack, maybe corner pockets for accessory storage or to fill with sand to weigh down.
 
 
