Just found a new bar/grill in the Shida area this weekend. It’s called HJS’ Fresh Grill. T.C. Wang, one of the co-owners speaks fluent English. The menu is simple. Focuses on Hsin Jian (Xinjiang) cuisine, hence its name.
I had the grilled chicken and a really good salad (the only non-Hsin Jian item). Interesting mix. Delicious. Not a place for vegetarians though. Prices are low. Great design. Address: No. 139 Chao Chou St. (02) 2322-5169. Have a taste. 
Finally went there over the weekend after reading the above post as well as the good review on a local food critic’s blog. Definitely recommend it. A cozy little place with BBQ style food from exotic Xinjiang Province. The chicken, served on a skewer, was fabulous (you can also have mutton, calamari, mushroom on a skewer), and the sticky rice is a musteat too. Price is about $350/person. The location needs some clarification though. The OP said Shida area, but it’s not the Shida night market area. It’s near the corner of Yongkang and Chaozhou, which is north of the Shida campus. I doubt there’s any other restaurant in Taipei that offers Xinjiang fare.
Someone tell Erhu ASAP.