Can't you just quick travel there from the map? You can't go to Val Royeaux through the War Table after you finish that quest.
When you have the VIEW option, that means that map has more than one travel location.
You need to click VIEW, and on the map, choose a location, either a tent or compass icon. The button then changes to TRAVEL.
This works (years later but was having the same issue). It's screwy to me, but drilling ffrom world map to local map and picking a fast travel node within the map works.
It's not consistent with this though.
For ex, Skyhold has multiple quick travel nodes yet on the world map you only have to click on the Skyhold icon and travel, not pick a specific node (although that'd actually be nice since you never really want to be where you "drop" in Skyhold and usually travel again within Skyhold.
So I wouldn't say this is any kind of firm rule and one needs to be ready for whichever.
Anyways.
