Apologies if this has been asked before, but I couldn't find anything with a quick Google search.
As it's such a large area, there's quite a few of them. Here's just a sampling off the top of my head:
Various Maya languages in the Yucatan and Guatemala. Those still spoken include K'iche' and Kaqchikel in the highlands and Mam and Yucatec in the lowlands.
Nahuatl, the language of the Aztec empire in central Mexico, which likewise still has many speakers.
Quechua was the primary language of the Inca empire, though it may have been spread earlier by the Wari empire (~700 AD). It is currently the most commonly spoken indigenous American language with millions of speakers.
To the south, in the Bolivian Andes, Aymara was and is the dominant language.
I and other folk here can answer more specific queries about each.
hi! hopefully you'll get some more detailed replies, but you can get a start with this post
e: oh, here's another one.. most (all?) of the maps in the replies are for North America, but they may include Central (or at least give you some leads)