I've adopted Houston as a hometown-by-marriage. I had extremely low expectations the first time I visited, and to my surprise saw those dashed with the surprises around each freeway exit. It's all automotive, unzoned, and commercial; a pedestrian nightmare. Those same forces make it dynamic, creative, and delicious. The local American Institute of Architects handbook says that since everything is going to go, everything goes; Houstonians take pride in taking design risks secure in the knowledge that errors can be erased with the next hurricane recovery or neighborhood redevelopment..
The Contemporary Art Museum, CAM (http://www.camh.org/), is your best place to start. This will get you into the Museum District, and give you an excuse to head out to Montrose and the collection of museums that is the Menil. Take a non-rush-hour cruise around the inner loop, I-610, and see how America's 1950's automotive love affair was supposed to play out. Pull off into the Heights for the James Turrell skyspace that is the Friends Meeting House (http://www.friendshouston.org/). .
Hungry? The commercial ethos of the city has allowed the growth of hundreds of ethnic restaurants with amazing quality, price, and portion size - there's a good reason Houstonians are America's fattest folks. A lot of the best are scattered in strip malls around the city, but you can't go wrong with one of the ubiquitous offerings of the Pappas family (http://www.pappadeaux.com/pappasfamily.htm). For the extra frugal, get a Fritos pie and Chicago dog at James Coney Island (http://www.jamesconeyisland.com/): better than what you'll get in either Brooklyn or on Randolph Street. .
Rice University's Rice Design Alliance (http://rda.rice.edu/) is the local keeper of the design flame. They've taken it upon themselves to explain Houston to themselves and to us beyond the bayous. Their quarterly magazine, Cite, is the best ongoing analysis of the design and evolution of any American city. To help you catch up, the editors put out a collection of Cite articles, The Ephemeral City, in 2003: I got it as a Christmas present, and have been devouring it ever since. .
Houston's beauty doesn't come from the landscape (swamps), or a grand city plan (Daniel Burnham did not visit). Instead, it grows from the desires of millions of Houstonians' to make money by making great places to live. Followed across the country this would be a disaster, but as a municipal design lab, it's produced some unexpected greatness.