Carl,
Cowboys is the best by a pretty good margin IMO, however it is also by far the most expensive course in the area. If that isn't an issue, you should go play there. By doing so you will have played the top private and public course, in my view, in the Dallas area. Otherwise I would agree with the Tangleridge recommendation. I like it better than Indian Creek and Ridgeview Ranch (although both of those are good courses themselves), and The Bridges (which I like quite a bit) is too far a drive from downtown.
As for other options, I'm a fan of Texas Star in Euless (not too far from the airport), a very nice Keith Foster effort that along with Cowboys, The Tribute and Tierra Verde is at the top of public courses in the area, and a nice value to boot. In the downtown area you have 2 interesting municipal choices. Tennison Park, one of Trevino's early stomping grounds, is one. The Highlands course there was renovated by D.A. Weibring and is unusual for Dallas in that the terrain is fairly hilly (Dallas National is as well). The second is Cedar Crest, an original Tillinghast design that also was recently significantly renovated by Weibring. It hosted the 1927 PGA championship. Both of these courses are interesting and fun to play, but come with some of the issues common to muni's.