I have been having many of these same issues. Lag spikes in dungeons, towns, out in all the different zones. Here in the last week it has not been as bad, but I still suffer from it occasionally.
I am also having a problem with my moden randomly reseting whiling playing. It only does it while playing FFXIV. I can play any other game all day long and the modem is fine. Load up FFXIV and within an hour or two the modem will reset. This happens more often when in a dungeon. I am on AT&T 12mbit DSL.