The Original Ninfa's on Navigation is a great local spot close to downtown great food and drinks there. Also right next door is El Tiempo another famous restaurant that just opened about a year ago. Both have some of the best mexican food and margaritas in town! If your looking for a fun trendy place close to Midtown where all the fun young bars are then Gloria's Restaurant is also a ton of fun with great food. On Fridays and Saturdays they have a live band that plays salsa music and the whole restaurant turns into a dance club which gets very packed, but very fun. Its a very diverse young crowd, plus lots of local bar spots within walking distance. 

El Tiempo Cantina Restaurants on Richmond-  Founded by the grandson of Mama Ninfa, the inventor of texmex.  Smoked fillet beef fajitas are amazing. 

Houston has a ton of great Mexican restaurants. A few off the top of my head:

Cyclone Anaya's (nice strong margaritas. Go to the one in City Center if you can, great location.)

Ninfas (multiple locations, great food)

Torchy's Tacos (more casual, but amazing tacos)

Let's get to some real - read "more authenic" spots - Irma's, El Real, Spanish Flowers, and La Guadalupana Cafe' and Bakery.

Houston is synonymous with good Tex-Mex food.  You almost cannot turn around without hitting a good Mexican restaurant.  Two of my favorites, both of which now have multiple locations, are Lupe Tortilla Mexican Restaurant which is famous for it's fajitas and it's slogan "Es pretty good!" 

The other favorite is Guadalajara Hacienda which I love all of their Mexican adaptations to seafood and there is no better Fried Ice Cream.  

I will second the Lupe Tortilla-there are multiple locations so don't put too much stock in the map's location-look it up to find the closest to your stay.  I know it is a bit more tex-mex-but I have always loved Pappasito's Cantina-they have the best chicken fajitas on the planet!  Chuy's does a nice job too.  They were started in Austin-

Try The Original Ninfa's on Navigation for delicious margs and overall Mexican food, tacos ago ago for some delicious tacos, and El Big Bad for a wide variety of good fusion margs (don't recommend the food there)

Try Pappasito's Cantina, Ninfa's Mexican Restaurant or Fiesta Guadalajara ...

Escalante's Mexican Grille in Highland Village. Cyclone Anaya's Mexican Kitchen has the best tortilla soup.

Depends what your looking for, I personally love the chain Tex-Mex restaurant "Gringos." Great food, great price, and their Cadillac margarita is amazing.

My current fav is El Real (http://elrealtexmex.com/) located 1201 Westheimer Rd. The building is a former vintage theater, and they still play old b&w westerns on the walls. This place is very old school and has perfect brown enchilada gravy. Lupe Tortilla has the best flour tortillas and beef fajita meat. Definitely try for the original location 318 Stafford St

Arnaldo Richards' Picos on Kirby, El Tiempo

I prefer the small hole in the wall places personally! A taco stand will have the legit stuff you're craving, but there usually isn't much seating or margaritas. Try Chuy'sor Gringo's Mexican Kitchen, there's also another place beside the football stadium, but I can't remember what it's called. Pappasito's Cantinais great, but not the best margaritas and if you ask me, over priced for what you could get somewhere else. Hope this helps!

You can try Pappasito's Cantina, Guadalajara Hacienda,   also basic but good Los Tios Mexican Restaurant, Escalante's Mexican Grille ( kinda loud high energy concept)

Gringo's Mexican Kitchen