I used to live in Dallas, so here are a few ideas:
Not a jewelry shop per se, but my favorite store in Dallas (it has
designer jewelry among other things) is "Forty-Five-Ten" It's kind of
like a "Barneys," It's in a nice pedestrian-friendly area that has a
lot of shops & restaurants. (the web site is www.fortyfiveten.com
There is (or was) an incredible restaurant across the street from
forty five ten called Abacus, which is worth a try. Expensive, but
worth it (unlike some)!
Ylang Ylang is another shop that features designer jewelry: (the web
site is (www.ylang-ylang.com
The new Nasher Sculpture Garden at the Dallas Musuem of Fine Arts is
supposed to be excellent.
Wear your best clothes! Dallas is a city that likes to dress up, and
grooming is a highly respected art form....
(relieved to be back in more casual Houston....)