The typical tour of the Cusco region combines the city with the Sacred Valley and Machu Picchu in three awesome days, including the full Boleto Turístico. We recommend devoting five days to get the most out of your visit-including one day to get acclimated to the high altitude.
Tierras Vivas is an excellent tour operator in Cusco, and it's specialize in adventure tours, trekking/hikking rafting excursions and others in llama arsisted treks.
Several outfitters offer rafting trips on the Río Urubamba, close enough to Cusco to be done as a day excursion from the city. The river is navigable year-round, with rains turning it into a Class V from November-May, but a more manageable Class III the rest of the year. All also do multiday trips to the Río Apurimac, outside the Sacred Valley in the South of Cusco, during its May-December rafting season.
With so many tours in Cusco's streets hawking tours to Peru's most famous sight, it's tempting to just buy one in order to make them stop asking.
Anyone who offers as Inca Trail trek departing tomorrow should be taken with more than a grain of salt-Inca Trail walks need to be booked months in advance. Don't make arrangements or give money to someone claiming to be a travel agent if they approach you on the street or at the airport in Cusco or Lima. Instead choose an agency that has a physical address.