The Woodlands is about 45 min from where I live, in SE Houston. For the most part, it is nice out there.
As you said right now, the NHRA will be visiting Baytown (about an hour away) on April 8-11.
This is the good time of the year for the weather in Houston, but it tends to rain a few days a week.
You are about 30 minutes from Downtown Houston and 40 minutes from West Houston (Richmond strip, Wesheimer, Uptown) which are the happening places for Houston, if you like that kind of stuff.
Galveston (about 1 hr, 20 min) is ok, just don't expect Florida beaches.