The size adds to the appeal. On one hand it almost feels only one barrier stands between you and the other side. On the other hand, the scale is dwarfing, especially at night and when you look at the city in comparison.
I've never been to California, and not a lot of beaches in general so I can't compare. I can only really compare it to places like Ica, which are generally prettier. Still, in Lima itself you have conventional beaches along with cliffs, which attract people who want a seaside experience but don't want to deal with beachgoears or sand.
Went to a museum all about electricity. They had an exhibit where you can power some lightbulbs with a bike. My pedaling can only light three of them though.
Also in Barranco you can find art shops. This one has a mural by Jade Rivera. I bought a few prints but I can't find them.
An American-style diner. Dunno how it is though, heard it's OK.