I'm not a Lubbock resident, but when I was there for a few days earlier this year, my most memorable meal was at La Diosa. My companions (all Lubbock residents) said that there was nothing else like it in the city. A self-styled "bohemian cafe," LD serves Mediterranean tapas, wraps, homemade desserts, and local wines. I really enjoyed the trio of tapenades with crostini (as a shared appetizer), the spicy curry-chicken salad (as a main course), and the "very best coconut cake" for dessert.
By the way, because La Diosa is also a winery, their wines are for sale. This is an exception to Lubbock's law against sales of packaged liquor within city limits. So stock up on anything you like!
Here’s a link to their website: http://www.ladiosacellars.com
Enjoy your visit,
A few places I really like:
CAGLE'S STEAKS just about 10 minutes outside of town. Order the 1 1/2 inch ribeye
JALAPENO is a great Tex-Mex. Family owned with excellent tamales.
Just off I-27 at 50th St
Check out LLANO Winery. Its just outside of town. Some pretty damn good reds including Cabernet Reserve and Viviano, a Super-Tuscan style wine.
TEXAS LAND AND CATTLE is a chain just off the loop at University. But, their grilled smoked quail (3 to an order) is memorable.