I found a good list at houstonmuseumdistrict.org
Free Everyday:
General admission is free on certain days for these museums
Every Monday
- Buffalo Soldiers National Museum - FREE Monday 10 am - 5 pm
- Czech Center Museum Houston - FREE Monday 10 am - 4 pm
Every Thursday
- Children's Museum of Houston - FREE Thursday 5 – 8 pm
- The John C. Freeman Weather Museum - FREE Thursday 12 – 4 pm
- Houston Museum of Natural Science - FREE Thursdays 3-6 pm through summer (beginning Thursday, June 14). Thursdays 2-5 winter.
- Museum of Fine Arts, Houston - FREE Thursday 10 am – 9 pm
- The Health Museum - FREE Thursday 2 – 5 pm
- Houston Zoo-The Houston Zoo offers free admission to our guests on the first Tuesday of every month from 2 p.m. until closing.
- Bank of America cardholders receive one free general admission on the first full weekend of each month. See here for the fine print. Weekends coming up are Nov 3-4, Dec 1-2, Jan 5-6, Feb 2-3, March 2-3, April 6-7.
Of course not everyone is going to be able schedule their visit during the free times, but if you look there are discounts available than just the 9 day Citipass you will see advertised everywhere. Here are the ones I have found for the more popular Houston attractions...
Health Museum savings coupon. Buy one get 1/2 off exp. 2/17/13
Houston Museum of Natural Science Corporate rates
Save over 50% on permanant exhibit entry to Houston or Sugarland. Discounts on Butterfly house and Planeterium and other current films and special events.
Johnson Space center Buy your tickets online and save $5 a ticket. If you live in the area it would probably be a great deal to buy a years membership for only $3 more than what you would pay at the gate to get in.
The Houston Zoo's website has a very long list of discounts available. Not super great discounts, $2 off adult tickets and $1 off a child (seriously only 1 and under is free?) if you pre buy them at Fiesta or are members of AAA.
but If I find anything else I will update the post. However at this rate I think we might try for the free times...
I'm off to hunt for some more.....