I just spent last Sunday in La Punta, Callao. There was once a large Italian community there, and there are enough old timers still around to support a good handful of authentic Italian restaurants. We went to two. The first was a bakery called Panarello. It serves up the usual chicharron but also has a couple pots of pasta dishes bubbling away. https://www.facebook.com/FamiliaPanarello
. We just had coffee and a bun there, but saw a lot of old timers noshing on ravioli. Innexpensive and nothing fancy. Then, we had a nice meal at Taller Razeto. The owner is of Italian descent. Really, really good food, and a nice location right off the boardwalk. More highbrow than the first. Dishes were in the 30 to 40 sole range. https://www.facebook.com/taller.razeto/
The owner was the one who attended our table, which is a nice touch.
I can also suggest the Osteria del puerto. It is on the first floor of a funky building full of art galleries, quite close to Plaza Grau in Callao. Prices are in the 20 to 30 sole range. Owner is also on site, making sure everything runs smoothly here, too. https://www.facebook.com/OsteriaDelPortoCallao/
Again, you need to go to La Punta, but that's a pretty nice excursion in its own right.