I'm a fan of "the emperor's favorite Shochu" which is called Hyakunen No Kodoku. It's a very nice wood barrel aged Amber colored Barley Shochu. May even be my favorite. It's like a very clean, smooth scotch. Tastes of caramel with a very clean finish. (No taste of peet)
You can try some at the Shochu bar on the 8th floor of Yodobashi Camera in Akihabara. It's around the corner from Unasho and the Kanji looks like this 芋蔵. (translates to Potato Storehouse or Collection or even Posession, not 100% sure)
They also have tons of other Shochu to try while you're there. Although I have never seen any Shochu cocktails which I would totally skip in favor of trying mind blastingly good Shochu.
Seriously? What you're asking for seems to be mutually exclusive. Quality shochu bars might serve shochu cocktails, but that's not what you go there for. You go for the variety of high quality honkaku (artisanal) shochu they might showcase. Do high-quality sake bars serve saketinis? Possibly, but most likely it won't contain high-quality sake. The way connoisseurs enjoy shochu is with either on the rocks or diluted with hot or cold water.
Here's a listing of shochu bars from Gurunavi. If you look at the drink menu at most of them, you don't find a menu of shochu cocktails, but a manu of honkaku shochu. Many of these places are in the category of "dining bars" serving food to go with shochu.