Cusco isn't the best place for shopping because things cost expensive.

Cusco city specially is magic for example when you walk in night, feel a air the most beautiful, but cold or when you walking in sacsayhuaman is a better experience, Cusco is quite quiet but in the night the streets is full.

Many places in the city as koricancha, temple Belen and other are quite beautiful for visiting during day.

My place favorite is Plaza de Armas which is ubicated in centre of city, has many places around it.

I think which city Cusco is the most beautiful the Peru, together a La Convencion

For extreme sport also there many places where can practice for example mountain walking, and mountain biking and parapent etc.