On the rental car - you may want to take one for a day and do the "drive around" that may include the San Gervasio ruins or Tequila Museum (along the northern road, the Transversal), the east shore, Parque Punta Sur and the southern beach clubs like Playa Palancar. If you drive a stick, Rentadora Isis on Ave 5 bet. Calles 2 & 4 offers VW's at $35-40 including the insurance. Closer to you, Less Pay near the Hotel Barracuda has reasonably-priced beater jeeps. Your Mastercard policy doesn't cover as much as the Mexican plan, so always buy the extra insurance which comes with Spanish-speaking personnel to help if you have an accident.
Food runs the full spectrum of prices and most is very good. You should try a tacqueria -- El Pique (across from the San Francisco market on Av. 30), El Foco (Ave. 5 near Suites Colonial at the square), Los Otates (much more than tacos - Ave 15 between Calle 3 & Salas.)
For arrachara or carne asada, there's HC Monterrey on Ave. 5 behind the mall and Parilla Mission on Ave. 30 between Calles 2 & 4. The last is an institution in Coz & also has really good Chiles Relleno and other dishes. Al Pie de Carbon is a small place that grills meat outdoors and is very good - corner of Ave. 5 & Calle 6.
Great seafood in town may be found at La Conchita del Caribe on Ave. 65 between 13 & 15 -- but it closes at around 4pm. But there are tons of other places. La Parroquia is in limbo -- it's been moving around due to construction -- last known address was in a wood shack near the clocktower in the square.
Others: Plaza Leeza, Mosiacoz & Casa Denis in the square; Guido's on Melgar Norte (upscale/Italian); La Cocay (upscale/continental) on Calle 8 bet. Aves 10 & 15; Kinta (upscale/continental) on Ave. 5 Norte between Calles 2 & 4; Tony Rome's Embassy (excellent margs) on Ave. 5 between Calles 3 & Salas. Le Chef at the corner of Ave. 5 & Calle 5; El Moro on Ave. 75 Bis (take a cab.)
Everyone does take out & doggie bags.
Have fun!