You might need to fortify the glass with tables or bookshelves, plentiful in this building, but there's not likely to be a million people in the library when the zombie contagion spreads like an evil cloud throughout Houston. In a pinch, a heavy book could double for a bludgeon if one of the undead manages to shamble in before you secure the place. There's probably a decent break room for the library staff, maybe with food.
5. Lakewood Church - 3700 Southwest Freeway
Yeah, I could make a mean joke about it being full of zombies already, but instead of going for the cheap laugh let's look at the actual building itself. Looks pretty sturdy and comfortable to me. It probably has a nice kitchen area, living quarters, and stored food and water. I'm thinking The Summit...er..."Lakewood Church" would make a pretty good place to barricade oneself from flesh eating zombies if a person or small group could get in the place. The downside would be that it's bound to be a magnet for people seeking spiritual answers to why the dead are rising from their graves, so it might get crowded fast.
4. The George R. Brown Convention Center, 1001 Avenida De Las Americas
Two words. Gun show.
Yes, this one will hinge on the timing of the zombie apocalypse, but if it should occur on a weekend where the Convention Center is having one of its giganto gun shows, you are in luck. Not only will there be access to a huge collection of guns and ammo to dispatch the living dead, but you're likely to encounter a lot of people itching to take out a bunch of zombies. In a few cases, maybe a few folks that have been planning for just such a thing to happen. There's also going to be access to food, and probably more than one booth selling MRE's and other survivalist chow.