If ya'all are fisherman, catching Redfish or Speckled Trout on the Texas Coast is a ton of fun. Guides would run ~$150/person or you could get completely outfitted with cheap gear for about $40/person and go yourselves. Boardmail me if you are interested and want advice on where to go.

Brazos Bend State Park has a lot of alligators and pretty swamp scenery. Lots of good "hiking" trails.

If museums are your thing, the Museum District is not far from NRG and has a lot of options. We just happened to go to the Natural History museum the day weekend of the BYU vs Houston game a few years ago and there was a lot of BYU fans.

Downtown is not the most exciting place. Definitely does not have the personality of a city like New Orleans or San Antonio. I would avoid it unless going to grab a bite to eat.