this is actually family-owned eatery. it is located outside the city(visiting with trustworthy people only!). the unique thing about this cafe is that all the seats are located on top of mountain spring river. the water is running under your deck while you eat delicious local cuisine. :)
Getting to/from Shymkent is a bit tougher now than it used to be. From Tashkent, take the metro to the Habib Abdullaev. From there, either walk or take a share-taxi to Yunusobod (there will be a metro stop there eventually). At Yunusobod, you need to take another share-taxi (marshrutnoe) to the border (granitsa), also called Chernaevka. Ignore the touts and their ridiculous taxi prices ($50 to Shymkent!) and walk across the border. On the other side, catch a minibus to Shymkent. Total cost of all this was about $5.50.
Out of Shymkent towards Bishkek or Almaty, take a bus to Taraz first and change there.