I had only one day in the City of Cusco but this is enough to get a climpse of the town. More days are only required if you would like to do some further tours outside of town (and there are plenty like the sacred valley tour and more). If you just want to walk around the old town, visit the monasterio or some museums one day should be fine.
I was a bit restricted of walking as I had a terrible muscle ache from befores day hike to Machu Picchu Mountain so I really took it slowly. My hostal (Inka City Hostal, 5$ including breakfast, comfi beds and clean) was around 15 minutes from the center. I believe it took me much more but it was because I was walking so slowly. Every step hurt my legs. So once I arrived at Plaza de Armas, the main square, I went for a massage. After walking a bit more I had a great veggie lunch menu (3$) and went on walking. I didn´t went uphill as this would have hurt too much but there are nice viewpoints and some ruins, only half an hour from the center. I spent the rest of the day wandering around, visiting the mercado artesanal close to the train station. This is the biggest one the and most recommended one as the prices are the best. Due to high competition you can get the prices you are willing to pay.
Cusco is nice, its a save place. In my hostal they said you can even walk around during night without any trouble. The plaza is nice and also the streets I saw. Additionally its cheap. Massages for around 7$ per hour, I had to buy glasses and paid 25$ – delivery within 2 hours and also got my hair cut (though you must be brave, I´m not too happy with the result but then, the hair will grew again) for only 3$.
I had a nice day, even got some rest and was now prepared of visiting Lima.
If you get cold easily like me, remember to bring warm cloth, especially for the night as it gets quite cold in the houses and they usually don´t have heating.