Look at the townhome/duplex development on Ambassador Row. It is in Dalworthington Gardens, 76013 zip code - south of the intersection of Pioneer Parkway and Smith Barry Rd. The police force is very pro-active, frequent patrols through the neighborhood and quick response time if you need them. I always felt safe because of that. A quick walk away is Veteran's park, or Green's farmer's market. A Walmart neighborhood market is maybe a mile away as well. Just a few minutes to UTA. We lived in Ambassador Row when our kids were little, and were able to rent a huge 3bed/3bath townhome for $850 a few years back. There are smaller units there as well that you can probably still get for under $800. One of my favorite parts of living in this community is the "Santa parade". A few days before Christmas, the entire police and firetruck force drive through the neighborhood at dusk with Santa on the back of a firetruck- lights and sirens going. They stop and let all the children visit with Santa. My kids LOVED that!
The elementary school is Dunn Elementary, if I remember correctly, which has a great reputation. There are also free half day 3/4yr old pre-k programs available at certain public elementaries around there, depending on your income.
This is a very family friendly area to live with lots of things for kids to do. Let me know if I can help you further.
