Reliant Stadium is a pretty good indoor venue for football, and you should enjoy watching the Gophers play there. I like it better than Cowboys Stadium in Dallas because it has more of a 'college' feel to it - more about the game and less about the big screen and corporate sponsors. There's not a bad seat in the house.
I didn't go to the game last year when we beat Northwestern, but I was there two years ago when Baylor got stomped by Illinois (I had free tickets, and watching the cubs fail is always a good time). We had seats in one of the club levels, which I highly recommend. The concession stands in the concourse back to the field and have full windows behind them, so you can watch the play on the field while waiting in line and ordering. They also have some nice lounge areas spread around.
There is light rail service connecting Reliant to the medical area, downtown, and beyond. Although Houston is a highly auto-dependent city, I would recommend getting a hotel along the rail line or parking and riding the rail to the game. After the game, the rail runs as well as busses which follow the rail line, and they don't seem to check for tickets.
There aren't a ton of bars or restaurants immediately surrounding the stadium, at least not in walking distance. The old Astrodome and the convention center are both on the grounds, so the stadium sits in the middle of a massive complex and a sea of parking. There is lots of room for tailgating.
Hobby Airport is much closer to Reliant, although IAH is much larger and nicer of a facility and may be closer to any non-downtown place you might want to stay. If you do stay up north, The Woodlands offers just about any chain retail and restaurant you could ever want. The Gallaria area also has lots of shopping an dining options. I'd suggest staying inside the loop (610) for more of a unique experience versus bland suburbs.
A couple of fun, off the beaten path things to check out while in town:
St. Arnold's Brewery - Named for the patron saint of beer, the brewery offers Saturday tours and tastings. Bring a picnic lunch or a pizza to enjoy while enjoying your beer.
Texas Junk Company - A secondhand store with a great selection of cowboy boots for cheap. Sometimes you can make some really great finds here.
Beer Can House, Orange Show, Art Cars - Three funky, artistic, and weird attractions that are uniquely Houston.
Houston Zoo - Even in Dec/Jan, the weather should be great for visiting. The Texas themed petting zoo area seems to be fun for kids. There is also a downtown aquarium, but it's a bit pricey.
Arts - There are world class museums and performing arts in downtown and beyond.
NASA Johnson Space Center
San Jacinto Monument - Not too far of a drive away; good for anyone interested in Texas history.
River Oaks - Older neighborhood with some great old mansions. Check out other Houston neighborhoods such as Montrose and Rice Village as well.
Tunnels - Minneapolis has skyways, we have 7+ miles of tunnels connecting downtown buildings.
Galveston - A short drive away, Galveston is a great town and sits right on the Gulf.
Aggieland - Of course, feel free to come visit the campus of Texas A&M University in College Station, just 90 miles to the north of Houston. I'd be glad to show you around.
If you end up in Houston for a bowl game, welcome and enjoy your stay. Feel free to ask me anything you might need to know to make your trip better.
