If you want to give your credit card some exercise, head out to Paseo de la Reforma, a popular place for shoppers in Miguel Hidalgo. You could also start your cultural experience by heading over to the museums in the area. It's also full of great shops and restaurants, so you can spend the afternoon having a wander. Splash some more cash at Avenida Presidente Masaryk.
You could catch an event at Auditorio Nacional, a stadium in Miguel Hidalgo. Hotels.com travelers also like the museums, art galleries, and cathedral in the area. If you think Auditorio Nacional is cool, you also might like Arena México and Plaza Mexico, both located nearby.