There are many seafood restaurants, but probably the safest is La Rotonda (Bolognesi 592, tel. 01/230-7266, 8 a.m.–11 p.m. daily, US$5). Apart from ceviche, the restaurant also does chicharron and grilled fish, serving on a second-story deck with good views of surfers on Pico Alto.
Another option is Cebichería Carmencita (Malecón de Punta Hermosa 821, tel. 01/9976-4792, 7 a.m.–10 p.m. daily, US$5), which serves a range of fish dishes; the owner will even set up a tent and campfire for you. At Señoritas beach, ask around for the ceviche stall run by Paco and Cecilia, which has a good reputation among locals.
For Italian check out Donde Luis on the Punta Hermosa [1] waterfront or, in La Planicie, Trattoria Don Ángelo (near control gate, tel. 01/230-7104 or 01/9740-9982, 7 a.m.–midnight daily, US$5). This is a family-run store and restaurant that serves pizzas and homemade pastas, including lasagna, ravioli, cannelloni, and gnocchi.
Links:
[1] http://www.moon.com/destinations/peru/lima/southern-beaches/punta-hermosa