I second the notion that you NEED a car to do anything in Houston.
I grew up North of Houston and now live South of Houston.
My work takes me over to JSC all the time and the tour is nothing special really. You get a look into mission control (its exactly the same as what is on TV) and see a few mockups. The tour at KSC is MUCH cooler. Space Center Houston is a waste of space unless you are 10 years old.
The zoo is awesome, especially since a private company bought it and refurbished everything. The Houston Museum of Natural Science is fantastic (www.hmns.org), as is the Museum of Fine Arts (www.mfah.org). Take a look at their websites and see what exhibits are going on when you are in town. You can get to the museum district and the Hermann park area via the lightrail train that runs down Main St.
I live south of Houston in Clear Lake and the Kemah boardwalk is always a good time.
Since you are going to be downtown anyways, you can take a tour of Minute Maid Park (Astros play there). The field is right next to the GRB convention center. I've taken this tour like 20 times (though you may not be as fanatical as I am). When the 'Stros aren't there they do tours a few times a day.
As far as night life, there are a bunch of places downtown, near Main St.
The Rice Village is a huge college kid hangout and is normally a great time.
I'd LOVE to get into the RTDA but no such luck getting a pass so far
spiffy