Tuxtla Gutiérrez (occasionally Tuxtla) is the capital city of Chiapas.
Tuxtla Gutierrez is a fairly new city. It has the main airport for Chiapas (located 30km outside of the city). The city itself is not particularly interesting. Ideally, you will want to move off to one of the more historic cities.
Ángel Albino Corzo International Airport (TGZ) is located 30km outside of the city. There are currently direct flights to Mexico City, Cancun, Monterrey, and Guadalajara. A taxi to downtown Tuxtla costs $20. Taxi companies have to pay fees to the Federal Government to operate in the 'Federal Zone' of the airport, as in most countries all over the world. Fares departing the airport will reflect that. You will have to buy a ticket for the taxi in the airport. Though colectivos do not come up to the airport itself, they pass by it on a road a short walk from the parking lot and cost considerably less than a taxi as they are not within the Federal Zone.
There are direct buses from Angel Albino Corzo airport to San Cristobal de las Casas. Times and prices can be found on the TicketBus website. As of May 2011, the price was 160 pesos and buses left early and mid afternoon, taking about an hour.
There is a modern OCC and ADO terminal that can be reached by Colectivo (Ruta 35) - ask the driver to stop or taxi from the centre for MXN 45. From there you can arrange onward travel to most destinations in South Mexico. If you are heading to Oaxaca, it is around 13 hours to Puerto Escondido or 10 hours to Potchutla (Zipolite or Mazunte) and it costs around M$500, you could always break the journey at Juchitán de Zaragoza (5h - M$222.00). If you buy your bus ticket in advance you could get up to %50 discount.
Frequent and cheap Colectivos serve most parts of town, you'll probably need at least a bit of Spanish to get around.
Go shopping. Tuxtla has many retail parks, with big retail chains such as Walmart etc present.
Visit nearby cañón sumidero which is biggest attraction around city. You can explore it from motorboat or from viewpoints above.
Things in Tuxtla are very reasonably cheap and affordable in the fact that it was set for the poor living standards of the indigenous that live there. Despite that, it is a very modern city with lots to do and see. There are plenty of shopping malls to shop in and items are very cheap.
The hotels in Tuxtla are generally of a very low quality and often quite expensive. If possible, you'll want to avoid sleeping in Tuxtla. Chiapa de Corzo is a good alternative city when looking for accommodation, and is only fifteen minutes away by autobus or colectivo.
Tuxtla feels fairly safe. Just exercise normal precautions.