Was just there recently, and I would ABSOLUTELY recommend the rental car route if you'll be there more than a day. Houston is very expansive, so a car is a nice way to explore and get to the Med Center (my program paid for the parking). Besides, if you sign up for a new account with Hertz (free of charge) and use the United Airline discount code (found on United.com), you can get a car for dirt cheap. I paid $40 for 2.5 days with a decked out mustang (i'm not a ford fan, but it was a nice way to get around). 🙂 Have fun.
p.s. to answer your actual question (sorry i'm a.d.d.): takes anywhere from 20min to 45 min depending on which fwy and time of day.