Though more tourists visit here as part of a tour from San Cristóbal de las Casas, the viewpoints over the top of the canyon are actually accessed from Tuxtla, and are convenient to visit from the city center if you have your own car. For more info on the canyon, see the Cañón del Sumidero article. Though the entrance (marked on the map in this article) is accessible by colectivo Route 69, the actual viewpoints are many kilometers up the road through the national park, and the staff at the tollbooth won't let you in without a car except during "athlete" hours from 6-8 in the morning. It's possible to tour all the viewpoints by taxi for 500 pesos (total per car), but keep in mind that you may get the same thing for cheaper if you take a tour through a tour agency that also includes the boat trip through the canyon.
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Games, rides (e.g. go-karts), replicas of pyramids and dinosaurs, etc.
Museum dealing with MesoAmerican history and history following the Spanish conquest in the state of Chiapas.
Paleontology exhibits specific to Chiapas. Tuesdays free?
A straight-up jungle right inside the city. Go for the forest experience, not for manicured flower beds.
A museum about the history of coffee along with various art and coffee sampling.
The city's central plaza, surrounded by the cathedral, state government buildings, and some cheap food options that stay open late.