Most portals are broken in current timeline, but there are alternate ways to get to many locations.
Alliance portals working: Pandaria, Draenor, Broken Isles, Kul-Tiras (important), Bel'ameth
Also you have a Honor Hold mage downstairs to get you to Outland
Kul-Tiras portal room goes to: Stormwind, IronForge, Exodar, Silithus (depending on Zidormi timeline)
Darnassus is one flight away from Exodar, and it has a Outland & Exodar portal in the mage area, and Exodar has a portal back to Stormwind.
I haven't explored Bel'ameth much, you appear next to portals to Stormwind & Mt Hyjal
Horde portals working: Pandaria, Draenor, Broken Isles
Unfortunately the Thrallmar mage downstairs doesn't work, nor does the Zuldazar portal
My horde alts not in active use, I often set their hearthstone to Zuldazar so they have quick portals to: Orgrimmar, Thunder Bluff, Silvermoon, and Silithus
However Orgrimmar Zepplin tower provides quick getaway to Undercity, which also has a Silvermoon city portal above ground.
A quick flight down the sewers into the mage quarters of Undercity will provide a portal to Outland
Also your Dalaran Hearthstone is on a 20 minute timer. In the middle of Dalaran (Legion) is a portal to Aegwynn's Gallery, which also has portals to Wyrmest Temple (short flight to Dalaran - Northrend), Karazhan, and old Dalaran Crater (watch the drop!)
With all those portals, you can get most places except Oribos without swapping timelines.