There are many literary events in Houston,; here are links to online information about some of them. Going to readings is a good way to meet other writers, to get a sense of the social sphere writers inhabit, and perhaps to find opportunities to read yourself (particularly at open mic events).
This is the premier literary event in town -- the Inprint Margarett Root Brown Reading Series.
Inprint also has readings by local writers, followed by open reading opportunities.
The University of Houston Creative Writing Program has readings, but also, the literary magazine they host, Gulf Coast, has a series at the Brazos Bookstore.
The Houston Poetry Fest is many events every fall: readings, awards, etc.
Here's a single event at UH-Downtown.
Kaboom Books is Houston's finest surviving used bookstore -- and they host a reading series specifically for "nanofiction"!
If you're interested in the Poetry Slam movement -- the main site has more information besides this Verboscity reading series.
Check here for ongoing notices, particularly events at Borders and Barnes & Noble stores in town.