The name of this dinner show is the Tang Dynasty Palace Music and Dances performed at the Shaanxi Grand Opera House Xi'an. It is located a few blocks south of the Southern Gate of the city wall. This should not be confused with another popular dinner show in Xi'an show called the Tang Dynasty Dinner Show.
My wife and I very much enjoyed the show. We only got show tickets so I can't comment on the dinner food. The theatre was set up with tables set up everywhere (there weren't any theatre-style seats). Most of the crowd were Chinese so I felt comfortable that the show wasn't a tacky foreigner's tourist trap.
The show itself was a little over an hour that had 10 parts. Each part featured dancers, musicians, or at times, both. The sets and costumes were brightly colored and very beautiful. The songs and dances seemed to be authentic traditional Chinese and were entertaining. All patrons received a free show program that explained (in Chinese and English) each of the 10 performances. Also, pictures and videos are allowed.
As a musician myself, I particularly enjoyed the highly skilled panpipe soloist, the absolutely amazing "trumpet" soloist (he also had some sort of whistle/mouthpiece), and the percussion group.
Keep in mind that this is NOT an acrobatic show, it's a performance to showcase the music and dance of the Tang Dynasty. I don't know if it was authentic to the Tang Dynasty, but it was a very visually and musically appealing show - the kind you hear about and want to see when in China. I highly recommend it!