if you're not on a pvp realm and not flagged for pvp, you don't need to worry about cowardly members of opposite factions, but you should be prepared for mobs if you're in a highly populated area.

a peaceful place that i've found is just south of booty bay, off the docks,  also up in the northwest corner of the zone where it meets westfall.  no mobs, no players, although near booty bay, you will occasionally get some players.

fishing is supposed to be relaxing.  try to find places that are just that.  >:}