My suggestion is to avoid bars around the East exit of Shinjuku. There have been cases of a girl or a guy sitting with customers and helping them to order drinks, hide are really expensive as the customers discover at the time of paying.
The Shinjuku ward office is aware of the problem, and has responded by opening a tourist information center. The, you can find the names of reliable and reputed bards with price-marked menus for all drinks. Support in multiple foreign languages is available.