No. NG+ is exactly the same as your first run, just with all the items and stats you have gained. The point of it is basically just to let you finish up any quests you may have missed in your first playthrough.
Spoiler
Of course, once you kill the dragon again in NG+ and reach the post-game you will have those harder enemies spawn all over the world like before.
So post-game is when harder enemies replace the mooks in seabreeze in places like that?