Like a few of the other replies, hot and humid during summer, and humid during the remainder of the year. Houston is just geographically situated where it receives lots of rainfall, relative to, say, other parts of Texas. Exception being Texarkana, which is a swamp, IMHO
Don't even think of commuting between Houston and Galveston---I-45 is currently and perpetually under construction. I lived in the Houston area for 25+ years and construction was never finished on I-45! I was just there this past weekend, BTW.
There are many, many towns/subdivisions between Houston and Galveston (Pearland, League City, Clear Lake, Alvin, Friendswood, etc) which all tend to meld together, but possibilities abound if you need to be in both Houston and Galveston and live somewhere to access both. Just keep in mind, from a psychological standpoint, that Houston is a massive city, with a mind-boggling population. I, personally, really like Houston
I think two folks from CA would be welcome, and esp. in Houston. So, so very much to enjoy and see, it would take an entire thread to cover! Also, as mentioned, a healthy dressage and hunter/jumper community, too in/around Houston. Not so much dressage in Galveston itself, though, that I'm aware of.
My SIL attended UT Galveston for her physician's assistant degree. I knew someone who attended the Texas A&M University campus on Galveston, too. Both are quality higher learning institutions.