I'm sure you've read already about the Miraflores and Barranco districts. The former should remind you a lot of the USA in terms of the structured organization, cleanliness, and overall gentrified organization, and it's a comfortable if bit more expensive (on a Peruvian level) place to find some great food. The latter is the more colorful and bohemian district about 10 minutes public combi ride south from Miraflores. Both have pretty access to the Pacific clifftop boardwalk too, and are around 30-40 minutes direct from the historic center depending on traffic.

If you want to see something a little less traveled, try out Chorrillos. This district is another 5-10 minutes south of Barranco but feels like another world. It's quite nondescript in terms of a port area, but it's a fresh and calm breath of air for some of who have been in Lima for a while. You can walk up the little Morro Solar mountain (10 minutes from base to top, with stairs) in Chorrillos where you'll find the big cross that's lit up every night, a bunch of various other religious relics, and the newly inaugurated Cristo del Pacifico that will ring memories of Christ the Redeemer in Rio de Janeiro. Take pictures of the incredible panoramic view of Lima, stroll along the boardwalk, chat with some lingering locals among the charming colorful streets, and grab a plate of super fresh ceviche along the port (20-25 soles per entree as of last weekend). About 3 hours is a good amount of time to allot.

Have fun!

Connie
Peru For Less