With decent bike hire available at Pony Expeditions, Caraz is an excellent place to do some cycling. One spectacular ride is the Cañon del Pato, downhill all the way from Caraz to Huallanca (35km in distance with a drop in altitude of 800m). Once in Huallanca, you can catch a colectivo to take you and your bike back to Caraz (S10), or you can cycle. Beware, the road has 35 tunnels. Bring a head torch.
Another option is to get a colectivo to carry you and your bike up to Punta Winchus (S10) and then cycle back down to Caraz.
Alberto at Pony Expeditions can go through the logistics of both routes in more detail.