Oh, wow. La Punta is just... amazing. I went there about a month ago and it was extraordinary.
To the east of Lima we have a city called Callao. It can be a very dangerous area. However, all the way to the east, you will find a small district in Callao, called La Punta. If you know how to get there or have someone to take there (driver, Uber) you will enjoy it a lot.
The district is surrounded by the calm sea. Everyone's really nice. There are some people that have boats, and take you around the coast to see some animals for like 25 soles.
The food is fresh and great. I went to a restaurant called La Caleta, and it was very very good. The price per dish was around 35 soles, but if I didn't want to eat that much (the dishes were huge) they could make you a 25 soles version of the dish.
If you have a way to get there, please go. It's an oasis in the city. No traffic around, and it's beautiful. 100% recommended, and I'm glad you mentioned it!