Lima has only one airport called Jorge Chavez International Airport (SPJC). The Miraflores district (where the hotel is) is generally very safe, but the way from the airport to Miraflores may not be.
We don't recommend renting a car if you've never driven in Peru before. There are a lot of different options for booking transport, and generally it's inexpensive.
We highly recommend getting a taxi from the official taxi counters located right next to the baggage claim INSIDE the airport, before exiting to the public access area. Inside the airport you can pay for this taxi service with a credit card.
If you are a US or European Citizen, you don't need a Visa or any special paperwork to enter Peru.
Like Lima, Cusco also has only one airport called Alejandro Velasco Astete International Airport. When traveling domestically in Peru, we usually take LATAM Airlines. The flight is about 1 hour and 20 minutes long, and there are numerous flights to choose from (departures about every 30 minutes to an hour). You can go on bus from Lima to Cusoco but we DO NOT recommend it.
We don't recommend renting a car. We recommend taking a taxi from the official taxi counters inside the airport. Not all of the taxi stands inside the airport take credit cards, so please make sure you have cash (40 - 70 soles depending on size of car and location of hotel).