The Stockyards area, which is basically along Exchange Street and Main is safe during the day (my opinion). I'd take normal precautions at night, and go with at least one friend. It's a tourist destination, so they have to keep things relatively safe. The area around it and between it and downtown is an older area, just be normally careful in route, stay on Main St. We go there all the time.
Billy Bob's Texas is a couple blocks north of Exchange. (huge honky tonk).
Ask around for Joe T. Garcia's Mexican Food. It's about 3 blocks south of Exchange, a block east of Main, and is a FW institution, world famous. Eat on the new patio, it's great in the evening.
I personally would rather see pics of you, the margarita drink, and the mechanical bull .............. ;^)