The Woodlands area has two(I think) very nice dog parks. Maybe if you take a visit there you could see if there was a message board at the park or ask around. The park is quite busy this summer, I think you would be able to ask around while you were there.
I don't know of any dog sitters in that area...I only know about some in the downtown area and such! Good luck!
Here is the link:
http://www.houstondogpark.org/
Jessica