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Nature preserve and swimming pool. (May want to take a look at the color of the water before jumping in.).
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COCYTECH
A museum for all of the science lovers out there. Anthropological and zoological exhibits, etc.
A spacious zoo which hosts only animals that can be found in the region naturally. In fact many of the animals roam the area freely and are not kept in cages. Don't miss the Museo del Cocodrilo while you're here.
If you want some stellar views of Tuxtla Gutierrez, this is a great place to get them. Also has some stations of the cross stuff, and a Jesus silhouette within the main cross statue itself.
Another Catholic church, this one with notable stained glass and a painting. Lots of pigeons when you're hanging around the bell tower outside.
The state government buildings.
Games, rides (e.g. go-karts), replicas of pyramids and dinosaurs, etc.