I don't know of an app but it would be a good idea. It would probably work on postcodes rather than pub names. If you are over a largish area then
Traveline can help getting between two points and includes walking as well as buses.
Maybe the maps function on a smartphone could help and I suspect there's something that telss you where the nearest pub/bar is, although that would no doubt lead you around all the sponsored Cafe Rouge and La Tasca's in town.
The other way to do it is to follow RogerB's example. Print off 6 google maps, sellotape them together, mark all the pubs you want to visit and plan a route. This app works for the first 9 or 10 pubs but then becomes a bit unreliable :D
PS. Welcome to the forums