MissJoeyDFW

It depends a lot of what your interests are. If you go to Hard 8 BBQ as suggested prepare to smell like a smokehouse the rest of the day. Great BBQ, I live and work not far from there, but I always plan on going straight home after eating there and not out socially afterwards. You have to walk directly in front of the smoke pit to order your food.

When visiting Dallas you need to be aware that we are in road hell construction in and around the airport. Updates can be found on this website http://www.dfwconnector.com/index_flash.php. If you are going to go anywhere west of the airport like Grapevine, Southlake, Fort Worth I highly recommend you allow extra time and check out the traffic updates. If you head east to Dallas proper or northeast to Addison or Plano it won't be much of an issue once you clear the airport.

There is live music every night of the week in Dallas of nearly any type. You can find who is playing where at Pegasus News mentioned by Swag. http://www.pegasusnews.com/

There are a lot of restaurants and shopping in Southlake Town Square, twenty minutes from the airport, two hours if you go at the wrong time of the day or when a lot of lanes are closed.
http://www.southlaketownsquare.com/
Grapevine has a nice downtown, restaurants and clubs, 15 minutes from the airport, again two hours if it is rush hour and the lanes are jacked up.
http://www.downtowngrapevinetexas.com/
If you want to venture further west to Sundance Square you can burn an entire afternoon and evening in the area. Shops, bookstores, movie theater, coffee shops, restaurants and night clubs for later.
http://www.sundancesquare.com/
If you like festivals that Thursday is the start of Mayfest at Trinity Park.
http://www.pegasusnews.com/events/2011/may/05/222928/
The Dallas Arboretum is always beautiful to go to and Asleep at the Wheel is playing there that Thursday.
http://www.dallasarboretum.org/