Sorry for reviving an old thread, but adding my two cents. I just took Taxi Green from the airport - their desk is right after baggage claims when you exit the area (avoid the ones next to the car rental desks).

To Miraflores, the cost was S.50. The car was clean, the driver was a safe driver, so it was a good ride.

With any taxi driver worldwide, there might be rogue ones so there is always the risk of getting robbed.

One alternative is maybe to take an Uber, if you can get roaming data on your phone. There is Uber in Lima, and with something like Uber, if you ever get robbed or have issues, at least Uber has a track of who the driver was.

Around Lima, I have taken Uber as well as gotten my hotel/restaurant/museum to call EasyTaxi, which is like their local version of Uber. You have to pay in cash though, but the fare is sort-of fixed in advance. The cars have all been very clean, and they drive much safer than the crazy official taxi drivers in Lima, and cheaper too.