Use TaxiGreen from the airport - follow JohnnyColombia's directions to the stand. In all of my trips there I have always paid 40-50 soles from LIM to Miraflores, never more. Sometimes they try to bump the price a bit but stand firm at the 40-50.

I have never used an ATM there, so I cannot comment on that. I always change a small bit of dollars (usually a hundred) to get me through the first night and then the next morning I hit up a cambista on the corner of Larco and Benavides in Miraflores or a money changing business (several located along Larco)

Walking in Miraflores is safe. Use the normal precautions that you'd use walking around any city here and you will be fine. Don't flash your cash or valuables and you will be fine.

A tip for you should you take cash money there - get NEW or CRISP dollar bills (20-50-100's) as if they are old and worn or have ANY rips or folds they will not likely be accepted for fear that they are counterfeit. Also, make sure you check your soles that you receive from cambistas or vendors to ensure they're not giving you old or worn soles either.