Welcome to Tulsa, @Joel Kadlec. I believe the path of progress in Tulsa is downtown and surrounding neighborhoods, including the areas near the Arkansas River, River Parks trail system, and the Gathering Place, a giant $350 million park being constructed on Riverside Drive near 31st Street. You could also look at living near Peoria Avenue in the Brookside or Cherry Street (15th Street) areas because Peoria is slated to get a Bus Rapid Transit system with frequent (15 min) bus service in a few years. Current bus service is very infrequent (30-45+ min), so it could be valuable to be located near frequent service in the future.
We just bought a house in the Riverview neighborhood just south of downtown as a personal residence and moved in two days ago. Before that we were living in an apartment downtown. In my opinion, what's happening downtown and surrounding neighborhoods near the river has more potential to provide above average appreciation than outlying communities celebrating the arrival of the newest Sam's Club.
We have a one-year-old, so we considered schools. There are ways to get into the better schools in Tulsa and we are going to do whatever we can to make sure he gets into them. If for some reason we can't, we'll do what it takes to put him in private school. You might check out this podcast on the topic of urban schools for people who want to live in urban areas.