Anything related to the seventh Umbral Era (Grand Company quests, Primal Battles, Sidequests concerning Dalamud, etc.) will be gone once 2.0 hits for obvious reasons. The dungeons will probably still be there, but they might look different. The entire world map is getting a redesign.

As for your specific example, I believe Yoshi-P said Shposhae would still be in 2.0, but it will be instanced.