There are two main airports you can travel into. One is Dallas Lovefield Aiport and the airport code is DAL. The second larger airport is Dallas-Fort Worth Airport (DFW).
The Dart is Dallas's train system. The closest station is the Parker Station. It is a 7 minute drive from our home, and 2.6 miles away. The Dart Train station services the DFW airport with a train coming to the airport. For Dallas Lovefield airport (DAL) you have to take a shuttle the Love Link 55 operates between Dallas Love Field and Inwood/Love Field Station.
There are many great malls in Dallas - Stonebriar, the Galleria, Willowbend, etc. However if I had to recommend one - I would recommend spending time at NorthPark Mall. Take from Parker Station the Red line and get off at Park Lane. From the Park lane station take bus #402 to North Park Center and get off at North Park Mall at East Entrance. This will take about 50 minutes. Otherwise without traffic it is about a 20 minute drive from my house. This mall has a movie theater, great stores, and restaurants. Lots of hustle and bustle.