Stars' fan and former Houston resident for 22 years here. NHL Center Ice and those various online packages are your best bet. Houston isn't a very hockey-friendly city, unfortunately.
As for city advice, try the tex-mex. It's far better than anywhere else in the country (unless you travel closer to the border, obviously). The rodeo is a lot of fun and always has big names in concert. The Rockets and Astros are both highly competitive teams now, with the Rockets having two of the best NBA players and the Astros being World Series favorites currently.
The city is ridiculously huge spatially. Always check the map before you decide to go somewhere. I used to have to commute 1-1.5 hrs one-way just to play hockey - getting from one side of the city to the other is time consuming and long. The airports aren't really close to major population centers, either. I also recommend not hanging out in the areas around the airport.
There's a lot more, but I'll leave it at that. Feel free to PM me.