Palenque, Chiapas, México
The town of Palenque sits only a few minutes by bike, foot or bus from the ruins of the ancient Mayan city of Palenque. The ruins themselves extend over a huge area and are composed of many smaller groups of structures situated around plazas. The most impressive of these are probably the main plaza — which is surrounded by the Temple of the Inscriptions and the palace/observatory tower — and the Sun Temple Plaza.
The Temple of the Inscriptions is well-known for housing the sarcophagus and jade death mask of Pakal, former ruler of the city. Unfortunately, it's no longer possible to visit the inside of the Temple of the Inscriptions without a research permit. In theory, that involves applications via your university and submissions of your research to the government; in practice it involves 150 pesos to the right people.