I live in Dallas and have been to the Gaylord several times. The closest hotel is the Embassy Suites, but there are sever others within 1 or 2 miles (Hyatt, AmeriSuites, and one or two more). I wouldn't say these are in "walking distance", but they're not far at all. I'm sure the Gaylord can arrange for a cab for anyone feeling uneasy about driving back and I can't imagine the fare to any of these hotels being more than 5 bucks.
Most of the "airport" hotels are much farther away. Be careful about staying at a hotel that is outside of the city of Grapevine (where the Gaylord is located) if you want to be as close as possible.
Also, on the parking, PLEASE CORRECT ME IF I'M WRONG ON THIS, but the North Texas VCA has told it's members that the special underground Viper-Only parking is through VOI and NOT through the Gaylord. Further, the parking is on a first-come, first-served basis determined by registration order, but that there would be spots for at least 600 Vipers. If anyone has better info than this, please share the wealth.