When neighborhoods like Brookside, College Hill in Wichita, Highland Park in Dallas, etc. were built they were definitely suburban when they were built, usually on the far edge of the city limits or outside of them before later being annexed.
Oddly, it looks like Highland Park is considered a “town” and not a neighborhood of Dallas proper. Kind of like Eastborough, which when originally built was completely outside of Wichita and about a mile or two removed from the eastern edge of the city limits.