I'd second both the Nasher in the "arts district" downtown and the Dallas Arboretum and surrounding White Rock Lake.
If you venture to Ft. Worth, the Kimbell is excellent, both for its collection and for its Louis Kahn building. It was featured as one of Sister Wendy's short list of favorite museums in the world. IMHO, its the 3rd best in Ft. Worth, falling in line after its two neighbors, my favorite the Amon Carter (
http://www.cartermuseum.org) and the Modern Art Museum of Ft Worth (
http://www.themodern.org/). All three house collections that are quite distinct.
The Amon Carter specializes in American art and has one of the world's, if not the world's, greatest collection of Frederick Remington along with a huge and excellent photography collection. The Kimbell's is primarily centered around Wester European art from the Renaissance to the early 20th century. The Modern is exactly what its name implies.
Not far from Ft Worth's museums is the Botanical Gardens and the Japanese Garden (
http://www.fwbg.org/). The Japanese Garden is one of my old favorites. I lived in Dallas for some 25 years and made regular pilgrimages to "Cowtown", primarily for the Amon Carter, Kimbell, Modern, and Japanese Gardens.
Keep in mind that the Dallas/Ft.Worth Metroplex is huge. Plan your trips well. As a point of perspective, the entrance/exit driveway for the DFW airport is an 8-10 lane limited access tollway. For trips to downtown from north central Dallas and its northern suburbs, I recommend the train/subway. Roundtrip tickets (when last I rode it some 7 years ago they sold all day passes at a good price) are as cheap or cheaper than downtown parking.
