I've lived in the DFW area for almost 25 years. I don't live in Dallas; I live out by DFW airport, but I work just east of downtown.
I don't know of any trails in Oak Cliff. There might be some walking trails in city parks. The HS tracks in my area are open to the public, not sure if that's the case in Oak Cliff area. Not sure of exactly what area of Oak Cliff you're talking about, but farther south and west is Mountain View Comm College and I think there's an asphalt trail on their campus. Not sure about access to their track.
Both my kids went to public school in our area, but if I would have had to put them in a public school in Oak Cliff I would have been very concerned. The reputation of DISD schools is not very good and Oak Cliff is considered a low income, under-performing area of Dallas; that mix is usually a disaster for schools. My daughter actually went to a DISD fine arts magnet school in DISD during HS and she noticed the academic standards were much lower there. I would disagree with your associates that St. Mark's is "do or die". My opinion is that a DISD school in Oak Cliff would be near the bottom of the educational spectrum, and St. Mark's would be at the top of the spectrum, with several choices in between.
Regarding moving to Oak Cliff; do a Google images search of 'crime map of Dallas' and see what it shows for the area of Oak Cliff you're considering. The general reputation of Oak Cliff is low income, high crime, don't get caught there at night, etc., and in many areas of Oak Cliff it's a reputation that's well earned/deserved. That said, there are some areas that have huge, beautiful, old, well-maintained homes. The Bishop Arts district is a hip, trendy neighborhood in Oak Cliff that is experiencing some "gentrification".
Hope this helps; sorry I didn't have more RR info for you. A lot of this is my opinion, but hopefully it gives you an understanding of why you're getting the "raised eyebrows" from associates at work.