I'm half Peruvian and used to go down to Lima every summer. (biased aside) yes this is the city with the best food in LATAM, especially if you love chicken, ceviche, seafood, etc. If you're going down to Peru I would highly recommend visiting Machu Picchu and Cusco as well!
As far as skating goes in Lima, its a great scene. Miraflores in Lima is the most tourist/skate friendly- the big mall, Larcomar, overseeing the beach cliff side has great spots, lots of long ledges, flatground, ledges into banks, stairs, and curbs that you can skate all day long, cops don't bother you there. and then Miraflores skatepark is just a 5min skate down the road form the mall. There is also the Converse skatepark in San Borja which is huge and offers a lot of different obstacles and a gnarly bowl. There's also San Miguel skatepark and La Molina and a few other plaza like parks in Lima, definitely have a lot of options in the city lol.
Would also recommend checking out Legana Inc, local skatebrand/shop in Miraflores owned by Danny Falla, sick company and they would have a bunch of great suggestions too!
One other thing I want to stress tho is the pick pocketers, stick ups, and smash and grab robberies that happen far too often to visitors and tourists especially as you're leaving the airport. Def want to be careful and watch your surroundings when you're out in the city or leaving the airport. Seen tons of people getting their stuff snatched as they walk the streets from ppl on bikes, or getting their car window smashed at a red light in heavy traffic (traffic is a nightmare in Lima) and getting their bags taken. This is going to be the case in all major cities in LATAM btw so be mindful and hope you and your girl have a great trip, Peru and LATAM is a great place to visit!