I think for downtown, you'll be happier visiting the historic core along Broadway than hanging out near Staples Center. There's Grand Central Market, The Last Bookstore, The Ace Hotel, lots of restaurants, cafes and shops.
And definitely do that bike ride down to Manhattan/Hermosa and back. Stop in downtown Hermosa or Manhattan for lunch or coffee or ice cream, watch some volleyball, walk around the village or out on the pier. Those are nice places for a short visit.