290 looks like your best bet—you’re going to go through Houston anyway (going around would add a lot of time, given road speeds), and 290 is the shortest way to get there (and has less traffic than 10).

http://tinyurl.com/meg86j

I disagree with barumonkey. Whenever I travel Austin to Houston I always take Hwy 71 -> I-10. 290 has a lot more stop lights and if it’s in any sort of rush hour you’re totally screwed. I lived in Austin 5 years, and now I live in Houston, so I’ve taken both routes numerous times. Beyond that, I-10 is the way to go from Houston.