Below you will find a quick outline of the more notable quests for patch 2.1. Use it to hit the ground running as soon as the server is up:

New Storylines
Main Story "The Price of Principles" - The Waking Sands (x:6 y:6) Minifilia
Hildibrand "The Rise and Fall of Gentlemen" - Ul'dah, Steps of Nald (x:9 y:8) Wymond

Daily Beast Tribe Quests
Sylphs - East Shroud, Little Solace (x:22 y:26)
Amalj'aa - Southern Thanalan, Ring of Ash (x:22 y:26)

New Trials
Good King Moogle Mog "Hail to the King, Kupo" - New Gridania (x:9 y:11) Vorsaile Heuloix
Ultima Weapon (Hard Mode) "The Ulitmate Ballad" - Mor Dhona (x:22 y:8) Alys
Extreme Mode Primals "Primal Nature" - The Waking Sands (x:6 y:6) Urianger

New Dungeons
Pharoh Sirius "Sirius Business" - Western La Noscea (x:26 y:26) Diamanda
Copperbell Mines (Hard Mode) "Out of Sight, Out of Mine" - Mor Dhona (x:22 y:8) Hugubert
Haukke Manor (Hard Mode) "Maniac Manor" - Mor Dhona (x:22 y:8) Lauriane

New Raids
Crystal Tower "Legacy of Allag - Mor Dhona" (x:21 y:8) Outlandish Man

PVP
Maelstrom - "A Pup No Longer"- Limsa Lominsa Upper Decks (x:13 y:12) R'ashant Rhiki
Order of the Twin Adder - "A Pup No Longer" - New Gridania (x:9 y:11) Vorsaile Heuloix
Immortal Flames - "A Pup No Longer" - Ul'dah, Steps of Nald (x:8 y:8) Swift

Quality of Life
Aesthetician "Beauty is Only Scalp Deep" - Limsa Lominsa Upper Decks (x:11 y:11) S'dhodjbi

Also, because this may end up being important for tome/gil farming (or whatever else):

Treasure Hunting
"Treasures and Tribulations" - Wineport, Eastern La Noscea (X:21, Y:21) H'loonh

In regards to the issues with the FATES for the Crystal Tower quest line per the lodestone:

Currently, we are experiencing an issue wherein the FATEs that were implemented by Patch 2.1 are being affected by the other FATEs occurring in the same area, and cannot spawn fast enough to keep up with the number of participants, therefore appearing at a very low rate.

Because we have been able to determine the issue, we are currently working to remedy the situation. Tomorrow, on Dec. 18, 2013, we will investigate to confirm the situation, and on Dec. 19, 2013, for a brief period, we will carry out maintenance in order to increase the frequency of FATE appearances.

We apologize for the inconvenience and ask for your patience and understanding.