No. Both Lima and Cusco aren't particularly safe for any tourist arriving late at night, particularly if its your first time there.
Top recommendation for your first night: arrange for your hotel or accommodation to collect you. It might seem expensive compared to a taxi but its just one night and could easily help you avoid an unpleasant introduction to the country.
This is general advice I would give almost anyone arriving late at night into a new country that they don't know. It's what I do in most places on the first night when I travel with my family.
Hope that helps over 6 years ago