Just north of DFW airport - therefore easy access by air. Most larger hotels have their own shuttles to/from the airport.
Grapevine is more or less equidistant from both downtown Dallas and Fort Worth. SH 121, 114, 360 and IH 635 all converge in Grapevine (the "funnel").
Right now, the only rail to Grapevine is the "Grapevine Vintage Railroad" that runs between Grapevine and the Fort Worth Stockyards. More of a tourist attraction than anything else, too slow to use as transit.
There are future plans  to have commuter rail from DFW airport (through Grapevine) through downtown Fort Worth then ending in SW Fort Worth (Hulen mall area).
Also, DART (Dallas Area Rapid Transit) has plans  for a new light rail line (orange) through Irving and ending at DFW airport. Although it won't travel into Grapevine, it will probably have a park and ride just outside the city limits on the north side of the airport.
The Gaylord Texan has two nifty shuttles. One loop runs from Gaylord to the Grapevine Mills shopping areas, the other loop runs from Gaylord to the historic part of Main St.
Cowboys Golf Club. Owned and operated by the Dallas Cowboys, this is a very high-end course that offers all the amenities and a spectacular golf course. Fees range from $75 to $160.
Grapevine Wineries. Grapevine is home to many wineries (even a couple of vineyards).
Historic Main Street. A nice stroll full of shops, a theater, art galleries and a steam train that runs to the Fort Worth Stockyards.
Fish/Swim/Ski Lake Grapevine . Fish the points (such as in Oak Grove Park, look for birds) for sand bass. If the birds are working, the fun is on! Cast your slab and reel 'em in.
Catch some live jazz at Kirby's Steakhouse 3305 E. Hwy 114, Southlake  Ok, so it's technically in Southlake (but just barely)... Surprisingly good jazz acts in a small setting, very enjoyable. Regularly included in the KNTU recommended live jazz schedule. Oh, and by the way the food is awesome (expensive, but well worth it).
Grapevine Mills 3000 Grapevine Mills Pkwy, in Grapevine. Large indoor outlet mall with close to 200 stores, restaurants, and entertainment venues. Other major Dallas-area outlet malls are located in Allen, to the north, and Hillsboro, to the south.
Biscuit's Cafe 322 S. Park Blvd.  Great breakfasts. A better alternative to IHOP.
See the entry for wineries above.
Embassy Suites Dallas - DFW Airport North at Outdoor World, 2401 Bass Pro Drive, ☎ 972-724-2600, . Experience the perfect blend of comfort and convenience at the Embassy Suites Dallas – DFW Airport North at Outdoor World. The hotel is just north of the Dallas/Fort World International Airport in the charming suburb of Grapevine, Texas.
AmeriSuites Dallas/DFW Airport North, 2220 West Grapevine Mills Circle, (972) 691-1199,  Located just one mile from Dallas/Fort Worth International Airport and 15 miles from downtown Dallas.
Garden Manor Bed and Breakfast, 205 East College Street, (817) 424-9177, .
Either Dallas or Fort Worth. Camping in a number of State Parks within a two hour drive.