E.B.
Houston Arboretum has nice trails through the woods and a tiny educational center. Because it is all wooded it stays a bit cooler. There's a sculpture garden across from the Museum of Fine Arts- also the MFA has a sheet that you can get for kids-it has pictures from their permanent exhibits and the kids are supposed to go through the museum finding those pictures. MFAH is free on Thursdays (and always 68 degrees!) The Contemporary Arts Museum is also free and sometimes has some very weird/odd/interesting exhibits. I used to take my kids when they were smaller (4 thru 10) and now my 17 year old and his friends go to the museums on their own all the time.
The Water Wall at the Galleria is cool and supposedly you can go up to the top of Williams Tower (altho I have never done it...)
Here's a link- and just because these are museums- you might be surprised what your kids find interesting.
http://www.free-attractions.com/houston.htm
Also- in Lake Jackson which is just about 45 minutes from downtown Houston there is Sea Center Texas which is a tiny aquarium and also fish hatchery. Pack a picnic and keep on going to Quintana Beach - a tiny island with a very nice, clean, calm beach.
http://www.brazoria-county.com/parks/Quintana/index.asp
And depending on your kids ages- maybe it would be worth it to spring for a Children's Museum family pass for the year. One summer I did that with another family and every Thursday we would pack lunches and go to the museum- eat lunch outside, let the kids play in the water feature there, maybe play in an exhibit and then come home to Sugar Land on the contra flow lane. Through out the years with my kids I have had a lot of museum memberships- whichever museum we belonged to was the one we spent lots of time at that summer.
And - if you just need to get them out of the house and away from the TV- Chik Fil A can have healthy food and always has a nice play area. We used to spend one day a week eating lunch out and playing the afternoon away. Now that they are older I use the beach like that- pack them up and say "call a friend, you've been on the computer too much, we're headed to the beach". Surfside/Quintana is an hour from Sugar Land and a cheap easy way to spend the day.
Good luck....I'll be checking back on this to see what other people suggest. I need ideas for my teenager with no job that has a girlfriend- places he can take her where I'm not paying for them to hang out...lol.