1. Visit the Macroplaza - This is the largest public square in Latin America and is located in the heart of Monterrey. Here, you can find iconic buildings and monuments, beautiful fountains and gardens, and views of the the nearby Cerro de la Silla mountain.

2. Go on a brewery tour - Monterrey has a long history of brewing beer, with several renowned breweries located in the area. You can go on a tour and sample some of the best local craft beer.

3. Explore the museums - Monterrey has several museums, including the Museo de Arte Contemporáneo de Monterrey, which is dedicated to contemporary art. Other options include the Natural History Museum, the Museum of Modern Art, and the Technology and Science Museum.

4. Take a day trip - On the outskirts of Monterrey, you can find several small towns and villages with great views and historic attractions. Consider going to Ciudad Miguel Alemán and the nearby Guruvayur Temple, or head to Santa Lucia Riverwalk for a peaceful day out.

5. Enjoy the nightlife - Monterrey is known for its vibrant bars and clubs, so be sure to experience the city's renowned nightlife. There are also plenty of live music venues, from small cantinas to large concert halls.