Dallas is a huge area and there are lots of nice neighborhoods to live in. I have lived in the Dallas area most of my life and have lived in various different neighborhoods. It really depends a lot on what matters to you and how much you can afford. Dallas Independent School District is a mess! There are quite a few awesome Elementary Schools like Stonewall Jackson (M-streets) Lakewood Elementary, Hexter Elementary (near White Rock Lake), but you would likely need to do private school beyond that, with a few exceptions - Woodrow Wilson High School in Lakewood is making a come back and Booker T. Washington Arts Magnet in Downtown Dallas is great if your child is interested in the arts.
If you can afford it, Highland Park is in the heart of Dallas just minutes from Downtown and their schools are all Exemplary. But there is a lot of pressure to be wealthy and successful - what clothes you wear, how big is your house, what car do you drive, etc. - which may not be the values you want for your kids. One of the gems within the Dallas City Limits is the Lake Highlands area because they are inside the loop (635 freeway), but are in Richardson Independent School District. This would be a much cheaper version of Highland Park, but with some of the same emphasis on status. Outside of Dallas proper, there are many nice suburbs - Richardson, Plano, Garland, Irving, Frisco, Coppell, etc. All have nice areas and some good public schools. I agree that you should avoid Central Expressway (I-75) corridor for getting to and from Downtown Dallas. I live in Garland and it is much less expensive than many of the other suburbs and has some excellent schools. Coppell is a newer suburb that has excellent schools and a wide price range in homes.
Chances are that you will be pleasantly surprised at the lower cost of housing in the Dallas area as compared to many other parts of the country. You should be able to find a pretty nice home in many areas (except Highland Park) for under $250,000. Definitely rent something until you find what area would work best for you. I should think you would find some nice apartments or homes to rent in Lake Highlands and lots of good daycare in that area. Also you would have the ability to get Downtown without having to take a major freeway. That would be a good place to begin, in my opinion. Good Luck and welcome to Big D!