There are a number of suburbs in the Dallas-Fort Worth area that meet your desired criteria. Since these cities aren't concentrated in just one area, I've grouped the communities by their relative location in the metropolitan area.
In Collin County, north of Dallas, the cities of Allen, Frisco, and McKinney are very popular communities that are desirable. According to recent population estimates by the North Central Texas Council of Governments, 80,400 people live in Allen, 100,800 in Frisco, and 121,850 reside in McKinney.
Northwest of Dallas in Denton County, Lewisville, Carrollton, and Corinth are nice. The Colony and Little Elm are faster-growing communities with reasonably priced housing.
In the eastern suburbs of Dallas, Rockwall has become a popular destination for newcomers. Forney has grown considerably as well. Mesquite and Rowlett are larger, more built-out suburban communities, but both have well-kept neighborhoods and other amenities.
To the south of Dallas, Cedar Hill is a nice community with lots of retail/shopping and recreational opportunities as it is located on the eastern shore of Joe Pool Lake. Other area cities that have experienced rapid population growth and lots of new home construction are DeSoto, Lancaster, Glenn Heights, Midlothian, Red Oak, and Waxahachie. All of these cities have nice, safe neighborhoods.
In neighboring Tarrant County (Fort Worth is the county seat), Mansfield, Hurst-Euless-Bedford, Keller, Burleson, Crowley, and North Richland Hills are nice cities.
The Dallas-Fort Worth area is quite large in size, so if you do decide to move here, factors such as place of employment and desired commute time should play a major role in your final decision on where to live.
Hope this helps!