If you're going to stay downtown, I think you can get away without a car. For the light rail, which ran frequently, you either buy a "Q ticket" from a retail outlet (and recharge at the rail stops) or buy one way tix at the rail stops - cash or charge. I think those were $2/ride. More info here:
METRO - Metropolitan Transit Authority of Harris County, Houston, Texas. We were told it was not a good idea to take the bus.
We just visited during Stampin' Up!'s leadership meeting and went to the Holocaust Museum -
Holocaust Museum Houston. It was well worth it. Didn't make it to any of the other museums but there are many in the museum district.
We went to the Zoo; it was just okay. Lots of the animals were nowhere to be seen in the chilly weather the day we went.
A visit to Phoenicia (grocery store on steroids)/MKT BAR (on the other side of the store; they had great gelato) is also worthwhile -
Phoenicia Specialty Foods. This was within walking distance from our hotel.
We probably didn't know where to go to look but found very little shopping where we were staying near the Convention Center. Perhaps it was more that we just didn't find anything we wanted. There was an outdoor craft fair in Discovery Green the Saturday we were there.
Enjoy your trip.