If your relatives are outdoorsy types, then Vegas in mid-January is an excellent time to explore the nearby state and national parks. Red Rock Canyon National Conservation Area is a great place to explore by car, horse, bike, or foot, with the added bonus of Red Rock Casino being nearby in case you want to ditch the family.
If you're up for the drive, Death Valley has fantastic weather now so you can enjoy its sights without worrying about heat exhaustion. And if they like skiing, Mt. Charleston with all its recent snows might work as well.
Personally, I'd just tell them to meet me at the video poker machine where I've planted myself when they're done doing whatever it is they were doing.