Monterrey has a metro system with two lines that cover the main axis of the city — from the bus terminal in the north through the centre to the southern suburbs. It is clean, cheap, and reliable. Most of the major sights (Macroplaza, Barrio Antiguo, Parque Fundidora, the brewery) are within easy walking distance of a metro station.
For Chipinque Mesa and the Santa Catarina Canyon, you will need a taxi or a car — neither is served by public transport. Uber operates in Monterrey and is generally reliable. The city is large and sprawling, and distances between sights can be deceptive; budget for taxi or Uber rides if you want to cover ground efficiently.