Houston's mainstream cultural heart lies downtown in the Theater District (http://downtownhouston.org/district/theater), at the intersection of Smith St and Texas Ave.
Elsewhere, especially in Midtown, you have plenty of choices for theater as well live music at clubs and concert halls, though Texas country is surprisingly scarce.
Look for event listings in widely available, and free, independent weekly Houston Press (www.houstonpress.com).
Two websites track local live music: Houston Music News (www.houstonmusicnews.net) and Space City Rock (www.spacecityrock.com).
Houston has teams for all the major pro sports.