Abancay is part of Peru's Southern Sierra.
The Tourist Office is next to the Plaza de Armas.
There are daily buses from and to Andahuaylas, one of the closest airports . This journey takes 5 to 6 h hours on an unpaved road. The closest airport is in Cusco, a 4 and a half to 5 hour drive on a bus or a 3 and a half to 4 hour drive in a "colectivo" (taxi car)
Distances are short, so walking is your best options for getting around. If you need a taxi, don't pay more than 3 Soles (0,80 US$) in the city.
Avenida Arenas, which turns into Arequipa, is the main drag through town. You can find all manner of restaurants and bars along this strip. Also a market for picking up fruits and vegetables. There are also a couple of supermarkets along this street. Paralleling this street one block further uphill is another avenue with a fair amount of shops and restaurants, including a vegetarian one.
You can visit the Canyon of Apurimac (Cañon de Apurimac) and cross it on a hanging bridge. Take a bus towards Cuzco and exit after ca. 1h at the village of Curuahuasi. Then go to Cachora - you can rent mules,horses and guides (canyon depth approx. 1000 m - one of the deepest in the world)
If you have 3 days, you can climb the canyon at the other side and visit the recently discovered and only 30% excavated ruins of an Inca city (Choquequirao). Guides are easily found via the tourist office in Abancay.
From Abancay to Puquio the bus costs 40 soles and the first one of the day leaves at 12 noon (Palamino). The views and country along this route are great, but it is windy.