Houston has over 6,000 restaurants and arguably the most diverse food scene in the American south. The city's enormous immigrant communities mean you can find excellent Vietnamese, Nigerian, Indian, Salvadoran, and Korean food, often in the same strip mall. The Tex-Mex and barbecue are outstanding too.
Vietnamese food is disproportionately excellent. The Bellaire Boulevard corridor through Chinatown has dozens of pho houses and banh mi shops, with Pho Saigon and Les Givral's among the most reliable. For Vietnamese food that goes beyond the standard menu, Nam Giao (Westheimer) does excellent imperial Hue cuisine.
Barbecue: Houston's best is at Gatlin's BBQ (Heights neighbourhood) for traditional Central Texas-style brisket and ribs, or Tejas Chocolate + Barbecue (Tomball, 40 minutes north) for a more refined take. The Midtown institution Luling City Market is closer in and very good.
Tex-Mex: Ninfa's on Navigation is the original, where Ninfa Laurenzo invented the fajita in the 1970s. El Real Tex-Mex on Westheimer does the classics well in a restored movie theatre.
For the serious end of the food scene, Houston has more Michelin stars than any Texas city. Uchi (Japanese-American fusion), The Pass (tasting menu), and Nancy's Hustle (modern American) are consistently rated among the best in the country.
Budget: For the cheapest, most honest meal in Houston, go to the strip malls around Hillcroft and Bissonnet for South Asian food, or the area around Bellaire Chinatown for Vietnamese. $10 will feed you extremely well.