What is your destination? The MFAH has free outdoor parking, but it fills up quickly. The MFAH covered garage parking is $6 all day with proof of admission. You can also look for open street parking behind the CAM and around the Bell Park area or around Menil.
The MNS has free parking, too, and you can get lucking around Hermann Park. But I'd do the covered garage parking for $6, since that is centrally located between MNS, MFAH and CAM/Menil.
Are you going for the Soto show? I hear great things about it. Comes highly recommended, and this is a one time only show anywhere. This is like 10 years in the making Jesus Rafael Soto http://www.mfah.org/exhibitions/jesus-rafael-soto/ You can find a video about the making of it, too.
I'm tempted to fly into Houston just for this show <iframe width="560" height="315" src="//www.youtube.com/embed/976Ghk1Ue4E" frameborder="0" allowfullscreen></iframe>
It is not a show, it is an installation. Might even be the only time displayed in Houston because the materials degrade and to install again the whole thing would have to be refabricated (which costs a million or so).
I was at a bar once, this guy put his Ferrari in park near the door and threw the keys at a random guy and said, "park it old man". You should try that.
It's an "exhibition" The vid I posted mentions they hope it can become a permanent installation somewhere in Houston. I assume that will require it's own building and endowment. Maybe Menil will have to tear down a couple more bungaloes.