The laws of visiting houses of worships from other religions come from the Talmudic tractate Avoda Zara (see e.g., 17a) on the laws of idolatry. It is clearly prohibited to enter a house of worship from non-monotheistic religions (Rambam, Peirush ha-Mishnayos, Avodah Zarah 1:3; Shach YD 149:1).
Halachic decisors debate where Christianity (general consensus: forbidden) and Islam (general consensus: permitted) fit. There is no debate regarding idolatry and polytheistic religions (e.g., Hinduism, Buddhism) and it is clearly forbidden to enter their house of worship.
See here, here, here and here for more details and sources.
I do not believe it is forbidden to visit a non-Jewish cemetery. When asked before on MiYodeya, no source was found and I couldn't find a ruling preventing it.
Chichen Itza, the Mayan site you mention, was according to Wikipedia a place where
pre-Columbian Maya sacrificed objects and human beings into the cenote
as a form of worship to the Maya rain god Chaac
The question of visiting sites previously used for idol worship but not anymore was asked before on MiYodeya, the consensus answer is that it is permitted if it is no more a religious site. So the answer would depend whether the site is today used as a place of worship or whether any remaining Mayans use it for religious ceremonies.
As always CYLOR for any practical ruling.