Just left Dallas late last year after living there for 9 years.
I wouldn't live in the Dallas city proper, but the metroplex has a lot of good areas that are fairly close to everything, but be prepared to have to take tolls if you wanna get anywhere in a reasonable amount of time. Sprawl is real there. SRT (121) is a toll for the most part (north of Coppell) and 635 had an awesome underground tollway section, but it's expensive, although a huge time saver when trying to get in/out of Dallas pretty much any time save for late night. Because the toll section of 635 is underground (mostly), people are flying through there - if you're not doing 90, you will get passed in the left lane. There are no areas for cops to sit in that section, thus the hoonery. When I was commuting to Dallas from Coppell on my motorcycle I was very guilty of undisclosed speeds there
Places that are good and are close to Southlake:
Coppell - where I used to live. Awesome HS if that's a consideration for you. There's a mix of super wealthy areas and average apartments, but in now way that detracts from it. Overall a very centralized area with easy access to 635, 35, SRT. Those 3 will get you anywhere you want pretty fast. The ONLY downside to Coppell is the cross-traffic -- the people using Dentop Tap road to cut from SRT down to 635. This has created a traffic issue in Coppell, which has been somewhat addressed by widening Denton Tap in some places (widening turning lanes especially), which is better but not great. You WILL pay the 'nice school' tax here because a lot of folks want to live there due to the school, and so home prices reflect that, along with its centric location.
Grapevine - pretty much in the middle of Coppell and Southlake, nice town. Good areas and great access to Grapevine Lake from the south. Grapevine Lake gets pretty busy, especially with increasing populating in the last 10 years, but it's still an awesome place to walk/hike/bike trails or boat/swim.
Flower Mound - very nice area, expensive. About as expensive as Southlake, more expensive than Coppell and Grapevine for the most part. It's on the northern side of Grapevine Lake, which I consider the 'better' side due to less crowding and more quiet trails that are accessible from the backyard, depending where you live.
Roanoke/Trophy Club and Westlake are an option. I used to date someone from Roanoke and it's a pretty nice, quiet suburbia. Kind of a haul if you want to go to Dallas, though.
Keller is kinda similar to Roanoke I think but I don't have much knowledge on that.
There aren't necessarily areas to avoid here on the north side of Dallas, but you will see a difference in infrastructure maintenance level, lower median income levels, etc. in the following, although there are 'good' pockets in each:
Bedford, Euless, Irving, Lewisville, Carrolton are such examples; more blue-collar. The exception to Irving is the Las Colinas area - very nice locale. I'd recommend it, but that's getting more south of the airport.
One thing to keep in mind is that areas near the airport are often in the flight path of the aircraft. Living in Coppell, I was right to the south of the Coppell Highschool -- literally the back alley ran along the school grounds fence. I could hear planes overhead frequently through the day, but I didn't find it an issue, though some might. If looking at a place, hang out there for an hour or so if you can, and you'll have an idea whether it's an issue or not.
Outliers - Plano, McKinney. They are further along SRT, but within easy drive to Southlake. Both towns have great schools and have been booming. No idea how that reflects on home prices, but neither will be cheap, for sure. Also Denton - farther north and I35 is a bastard. No way around it, but, there are upsides. It's quieter, nice homes, great areas. Had a good friend living there and I really enjoyed it. It's close to Lewisville lake, which is a plus if that's your thing. There are great pockets of woods there with trails made by the locals, that aren't known to most people around. Those were my favorite spots for a quick day hike with the dog.
Linear Mode
