The conventional way to see Monterrey without a car: a registered agency (RNT 35190390019) running day tours with hotel pick-up since 2003. The pin is on the city centre; their office is on Avenida Hidalgo in the Centro.
The city tour covers the Macroplaza, Barrio Antiguo, a boat on the Paseo Santa Lucía and the old steelworks at Parque Fundidora in five or six hours. The others go out to the mountains: Cola de Caballo and the Pueblo Mágico of Santiago, the cable car up to the Grutas de García, Chipinque and La Huasteca with San Pedro, and a long day to the Grutas de Bustamante. They also do airport transfers, a mezcal tasting, the hot springs at San Joaquín, and day trips over the state line to Saltillo, Parras and Cuatro Ciénegas.
A second WhatsApp line, +52 81 1578 4824, is labelled for the office; the main one above is the booking chat.