There is an arcade in Dickenson (on the way to Galveston) that has a few classics, but when I stopped there in February many were not well kept up.
They had:
Ms. Pac-man (w/ a lcd....looked terrible)
Missile Command (track ball needed a rebuild)
Joust (worked well)
Centipede (charged 2 tokens for this one, only one for the rest)
Defender (in a Frankenstein cab)
3 player Off-Road (I didn't play this, but I think the monitor looked rather tired)
and several other newer games, but I went there to try out their classics.
It might be worth a stop if you're already heading down that way, it's right off I-45 @ FM-517