Astrid y Gaston is kind of a tourist trap now, but still an excellent restaurant and worth visiting to say you have been there. It used to be housed in a small house in Miraflores, and was closely run by Astrid y Gaston themselves. They sold the business, and it was moved to San Isidro in a much larger space with less personal attention. Still excellent food and a nice experience, but much more of a corporate feel now. My favorite restaurant is Rafael on Calle San Martin in Miraflores, also Cala on the Malecon in Barranco. Rafael Osterling also has a less formal brasserie a few blocks away from the Hyatt, Brasserie Felix. And the restaurant inside the Hyatt, Isidro, is very good. The big destination restaurants in Lima, the ones where you need to make reservations months in advance and pay the bill by selling one of your children, are Central in Barranco and Maido (for sushi) in Miraflores. For ceviche, I would suggest Gaston Acurio's cevicheria La Mar or Pescados Capitales, both located on Av La Mar in Miraflores.

Taking an Uber from the airport is kind of a complicated process and not for beginners. (I don't know if it's still the case, but at least until recently they were not allowing non-travelers into the airport, and locating the driver outside in the scrum of taxi drivers aggressively soliciting your business can be difficult). Much easier and probably the same price (60-65 Soles to San Isidro/Miraflores) to take one of the taxi services operating out of the kiosks in the arrival hall just outside of the customs area. Taking Uber back to the airport is easy although one time I was leaving the Hyatt very early (4 AM) and nothing was available with Uber so I had to ask the front desk to call me a car service. The car was very nice and I was pleasantly surprised to be charged the same as I had planned to pay by Uber (50 Soles).