Sure, the name is a tough sell (yay, let's go to the Finance Secretariat Museum!), but it's actually a very interesting place. The museum shows off works from its collection of more than 30,000 pieces of Mexican art, much of it contributed by painters and sculptors in lieu of paying taxes.

Built in the 16th century, the former colonial archbishop’s palace also hosts a full program of cultural events (many free), from puppet shows to chamber music recitals. The building sits atop the Templo de Tezcatlipoca, a temple dedicated to an Aztec god often associated with night, death and change through conflict. You'll see the temple's stairs just off the renovated main patio.