What we were planning to do is to stay in Lima the night of the 4th of August and fly to PM at 8.30am on the 5th. It's too risky to fly directly to PM on the 4th in case our international flights are delayed etc. as we'd only have a 2 hour buffer.
At the end of our trip we are planning then to leave Arequipa on the morning of the 20th of August and flying out then the next day at 11pm.
This basically gives us about 2-3 days total to see Lima in a disjointed way. We are planning to stay in Miraflores for the night of the 20th at least, but what would be the best option for the 4th?