The late Trammell Crow, who passed away in 2009, was one of Dallas’s best-known real estate developers. He and his wife, Margaret, shared a lifelong fascination with Asian art and together took numerous trips to China (the first in 1976, when few Westerners were issued visas to the country), Japan, Nepal, India, Cambodia and Tibet. From the impressive collection they amassed, more than 300 pieces are on display on three floors in a building opposite the Nasher Sculpture Center; among the highlights are jade ornaments from China, Japanese scrolls and a 28-foot-high sandstone façade from an 18th-century Indian residence. At once extremely personal and museum-quality, the Crow collection is a must-see for anyone interested in Asian art. Admission is free.

The downtown Dallas Arts District, whose centerpiece is an ultramodern performance center designed by Sir Norman Foster, has given buzz a new meaning. During the preliminary planning the city fought hard—and raised unprecedented funds—for the 68-acre complex, whose completion required some three decades. Then came the long-awaited opening, with a week-long series of celebrations and a flurry of reviews, both positive and negative. Now is the—perhaps most important— postopening period, when the new neighborhood must establish itself in a city more famous for football and corporate headquarters than for Shakespeare and Puccini.

The good news is that from an architectural standpoint, the additions to such Art District heavy-hitters as the I.M. Pei–designed Meyerson Symphony Hall and Renzo Piano’s graceful Nasher Sculpture Center are ambitious and innovative.

The Winspear Opera House (2403 Flora St) created by Foster + Partners, centers on 60-foot-tall glass walled lobby positioned under a steel aluminum-slatted drum intended to deflect the sun and create a cooler microclimate around the house. The bright-red drum rises above the solar canopy like a mod top hat lends a playful touch of color to the district. Inside, the state-of-the-art performance hall has some of the best acoustics in the country; even the stage curtain received special artistic treatment: mixed-media artist Guillermo Kuitca designed an abstraction of the seating plan that was reproduced on the fabric.

Across the street, the Wyly Theatre (2400 Flora St) is much smaller and more contained but no less stunning. Rem Koolhaas and Joshua Prince-Ramus’s sleek theater is clad in aluminum poles of varying sizes, giving the façade an almost fluid texture—like a rippling curtain frozen in space. New York Times architecture critic Nicolai Ouroussoff wrote that these new buildings “sit comfortably alongside older structures like I.M. Pei’s concert hall and Edward Larrabee Barnes’s art museum, extending the conversation across generations as well as contrasting architectural philosophies.”

Part of the downtown Arts District, the city’s major art institution, the Dallas Museum of Art, contains everything from ancient Mediterranean artifacts to contemporary art, although some collections are stronger than others (which has led to criticisms of lack of focus). In 2005 three prominent local families bequeathed to the museum more than 800 works of modern and contemporary art, significantly improving its holdings. Don’t miss the large Ancient American Art section, which displays ceramics from the Southwestern U.S., Mexico and Guatemala, gold from Panama, Colombia and Peru, and textiles and ceramics from Peru. Also worth visiting is the contemporary wing, which has several smaller galleries showcasing often-changing exhibits. The large windows of the soaring atrium—where jazz concerts are performed every Thursday evening at 6 and 8 P.M.—are adorned with colorful oversized glass flowers by Dale Chihuly, giving the whole space a charming Alice in Wonderland feeling. Closed Monday.

The phrase “jewel box of a museum” is certainly overused, but it perfectly fits Dallas’s exquisite Nasher, both inside and out. The small, light-filled museum was designed by Pritzker Prize–winning architect Renzo Piano and opened in 2003. The elegant building with just three galleries and leads into a leafy one-and-a-half-acre garden that was created by landscape architect Peter Walker.

The Nasher contains the private collection of Raymond and Patsy Nasher, both avid collectors of modern and contemporary sculpture, whose holdings feature an array of such big-name artists as Rodin, Brancusi, de Kooning, Giacometti, Matisse and Moore, among many others. In the hands of a lesser architect and landscape artist, the exhibits could have easily become best-of showcases, but the layout of the Nasher and the way the pieces are displayed create a compelling narrative. In one corner of the garden, the massive rust-colored steel slabs of Richard Serra’s My Curves Are Not Mad play off Jonathan Borofsky’s animated Hammering Man, which in turn towers over Magdalena Abakanowicz’s Bronze Crowd. I was familiar with the work of almost all the artists represented at the Nasher and yet left feeling as if I had seen them for the first time. If you have time for only one museum on your Dallas visit, the Nasher should be it. Closed Monday.