Though it's an old post yet, I would like to share some of my knowledge here for anyone who want to visit there without much pressure on your bank account.

Try visiting these places:
1. Bosque de Chapultepec: pack your lunch and plop down in grassy picnic area below the Chapultepec castle.
2. Palacio Nacional: It is a working government building that exhibits arts, dress and handicrafts of world culture.
3. Museo Soumaya: It's a piece of art itself. You’ll find yourself in awe of this beautifully crafted building, which is gilded with hexagonal discs of glimmering metal, creating a futuristic sleek shape.