We go to the one off Westpark/610 a couple of times a week. It's not the greatest -- it's pretty muddy all the time, but there's hoses and stuff to clean 'em off after.
In addition to the ones listed on that website, there is also an unofficial dog park along Buffalo Bayou at the corner of Studemont and Allen Parkway, although its not very close to Clear Lake.
My wife and I have been to both the 610 and Westpark and Montrose and Allen Parkway dog parks. I like both, although the Westpark one is more regulated, i.e. two areas for small and big dogs and it's fenced in. The other one, which is a block from my apartment, is wide open and all the dogs mix with one another.
I think if you go to the City of Houston's website you can find the list of dog parks in the city. It might be under the parks and recreation department, but I am not sure. Just go to the main page and start looking. Those parks mentioned are obviously a good ways from clear lake and there might be ones closer listed on the COH's site.
You could also see if Pearland or Friendswood have dog parks. I work in Pearland, but I don't know if there are dog parks around here. Same for Webster, although Webster is in Harris County, so it will probably be listed on the COH webpage if they have a dog park.
The City websites might have info too. I should know. My office does work for all the places I mentioned. Never look for dog park info, however.