Unfortunately, not much of Texas is walkable. Austin is doable by bus, and I bet you can get a ride to a few restaurants from PPKers if you want as well. The airport in Dallas is international, so you may be able to get a direct flight there. I've flown straight to London from there.
There are definitely cute shops and galleries in Austin. I also always recommend seeing an event at Alamo Drafthouse
. They're the movie theater that had that youtube video about kicking out a texter, and they do fun things like sing-a-longs and Master Pancake Theater. Seeing the bats fly away from the Congress bridge at sunset is fun, too. And swimming in Barton Springs.