Cheap Eats @ Houston Galleria
You didn't mention if you are a Texan or not, so I'm going to assume you aren't. If you are from San Antonio or something, then you probably aren't as interested in, say, my Tex-Mex suggestions...
There's a ton of Tex-Mex (and Mex-Mex) in Houston including near the Galleria. My favorite Tex-Mex place is not too far from Galleria area. It's called Taqueria Cancun and has multiple locations including on Gessner close to 59 South. While everything I've tried there has been amazing (and I've tried probably half the menu), they do shrimp the best. And there beef enchilidas with brown sauce are simply the best I've ever had. My typical order is two beef enchilidas (no rice or beans) and a shrimp quesedilla. It's a lot of food and not much more than 5 bucks.
As I've said there's a lot more Tex-Mex to be had, and most of it pretty good and cheap. Just experiment some, though you can't go wrong at Taqueria Cancun.
I guess we should talk barbecue first. IMO, Houston has little good barbecue to speak of compared to other parts of Texas. Still, if you aren't from here, then it can also be worthwile cheapish investment. Two places come to mind. One is Good Company Barbecue on Kirby close to 59. Their chopped brisket sandwhich with sauce on jalepano-cheese bread (the bread is not that spicy) is one the city's best bargains at just a little over 3 dollars. Their other barbecue I have mixed reactions about, but I will say that their half duck is a bargain even though it is the most expensive item. Half a duck is a lot of food, and it's definitely a unique barbecue item.
The other place, is Luling City Market which is on Richmond right inside the 610 loop. It could well be within walking distance of your hotel. This is an interesting place, because it's mother restaurant in Luling, TX, has drawn rave reviews on this board and other places. However, this cityfied place is not as good as the mothership. Still, if you want a taste of what "real" Texas barbeuce is like, this would be the place to go in Houston. The brisket and sausage are best.
Another place that isn't too far from the Galleria, is Barnaby's on S. Shepherd at Gray (or thereabouts). It's the kind of place that serves interesting burgers, meatloaf, and amazing apple pie. The lemonade is also a treat. All at reasonable prices. The place on Shepherd is the second Barnaby's and has more a "yuppie" feel. The original is in the Montrose area of town which is even further from the Galleria, but certainly has more atmosphere.
I would be remiss if I didn't mention one of my favorite places in Houston. It's another the Goode family line called Goode Co. Seafood. It's close to the barbecue place on Westpark. It's a seafood place that combines the elements make that Houston so unique food wise: Texan, Cajun, and Mexican. The best example is my favorite dish: the mesquite grilled catfish po-boy with pico de guao. A wonderful sandwhich for $7. The shrimp campachee is also super. The menu calls, it a Mexican seafood cocktail, and it's all that and more. Some of the fish dishes can be pricy, but it's the kind of place that has $7-$20 food. It's always crowded however.
If you are into Indian food, the Galleria is close to the Indian mile of Hillcroft and 59. Lots of places to choose from. I don't really have a favorite-- I usually went with others that knew more than I. Go to whichever is the most crowded would be my advice. There's a good, cheap South Indian food place called Madras Pavillian on Kirby just a little north of 59 that serves what I consider good Indian food. The place is a chain, I believe, but it's a good one.
There is also a very popular Vietenmese/Chinese place called Kim Son close to the Galleria. It's another restaurant with multiple locations and while I'm usually hesitant of those kins of places, there food is very good (and popular). I don't remember exactly where it is. I've included some links below to help you search for it.
The area that I call Suburban Chinatown is relatively nearby. It's center is Bellaire just inside the Beltway 8 loop. All kinds of "real" Chinese food. It's another one of those places where I usually just go to the most crowded place or let some of Chinese Houston friends show me around. I do remeber liking Lai Lai's.
That should start you out allright. Houston is a great food city and I don't think you'll be disappointed. If you have any certain food type requests, just ask. I'm sure I or someone else will be happy to help you.
As my memory is not the best, here's some links to find out more about locations, times, phone numbers of some the above restaurants:
I know I'll be razzed about these suggestions, but just trying to offer other options, though all above are excellent. There is a family owned cafeteria (don't laugh) called Cleburne's which has surprisingly good food in sinfully huge portions. The place is closed on Saturdays, but the rest of the time the long lines attest to the quality and value.
The other caferteria is Luby's at the N. Post Oak location across the street from Eatzi's. Food isn't bad and location is convenient.