As Tim says, it's Kannauj. Â
Rennell's "Bar" is probably "Barh" which is indeed about the right distance below (=downstream) from Patna. See the map: http://tinyurl.com/o2xpr64
The archaeologists focus on Kumrahar, which is a suburb of Patna, and a long way west of Barh. Other sites right within Patna are discussed and identified in the archaeological literature and the Gazetteers.
The Imperial Gazetteer (Oxford, Clarendon Press, 1908-1931) places Pataliputra between Bankipur and Patna, on the tongue of land between the rivers. See also here.
Dominik
