Things like carved pillars or painted statements on walls, if not actual documents. Specifically I want to know if there's a place online, or some book(s) or what have you, where I can read either the translations themselves or an analysis of them and what they tell us about their cultures of origin (as opposed to what's been sussed out from artifacts and paintings.) edit: Thanks you guys, you're amazing!
The folks over at the Foundation for the Advancement of Mesamerican Studies, Inc. (FAMSI) maintain a good number of public databases containing exactly what you're looking for. The Montgomery Drawings Collection contains a large number of stela illustrations you can browse through by site. I'm not aware of any single place that compiles translations, but if you find an interesting looking inscription, you can usually use the search box on the FAMSI site and find an article that uses the stela and translates it. I'd reccomend this if you're looking for one good source. It compiles inscriptions from the site Piedras Negras and puts them into chronological order. The author provides factoids related to the text and good "rough" translations. It doesn't have too many full illustrations, but I believe most are in the Montgomery collection if you search "Piedras Negras Stela/Lintel/Panel X." I'd also reccomend the Peabody Museum's Corpus of Maya Hieroglyphic Inscriptions. It contains a few translation, but the best features are the high quality illustrations (that you can overlay on photographs) and maps of where inscriptions were found.
For writing on ceramic vessels, you can use Justin Kerr's wonderful collection of photographs. Much of the writing is rather formulaic and uninteresting, but vessels do pop up with "word bubbles" in illustrations or captions for picture.
I'm no historian, but as far as I'm aware websites like FAMSI are good sources to start with, as well as David Stuart's blog Maya Decipherment on translating Mayan writing, several articles there are written by other famous epigraphers and archaeologists as well. Far as actual documents, well they mostly burnt or withered away as I'm sure you know, but in addition to a few surviving codices there are Colonial-era documents written by native authors and translated into Spanish and later English, some of which are possibly based off of Pre-colonial writings. The Popol Vuh is a famous example, but this site has a 1933 English translation of the Book of Chilam Balam of Chumayel written by some Maya writer in the colonial era.