Where your work is located is going to give you some great options. Pretty much anything really close to the TCU area is going to be a pretty good location, I grew up a little bit southwest of TCU.
But I've had a few friends (around 30 years old, some with small families) wind up in a pretty neat little area just northwest of the Camp Bowie/Montgomery intersection. It's a nice little affordable area that will put you really close to your work and the 7th street scene that has exploded. I squared the area in the picture below as best I could. These are going to be older houses which is more my style, just a heads up. I would think that area would fall in the 76107.

All of that info is coming from someone who has lived in Dallas for the last 6 years so take it for what it's worth, but I get back to Fort Worth quite a bit and spent my first 18 years there (I'm 30).