Levels 25 - 27 The Lower Abyss
When you reach level 25 you will want to drop everything you are doing and do the Abyss Attunement quest. The reason you'll want to go apeshit and rush into The Abyss is because not only when you kill a mob here will you get XP you will also get Abyss Points. Also, since it really is just a grind from here on out anyway what better place to do it then The Abyss.
(Will update this section right here with an Abyss attunement walkthrough when I do it again.)
When you get to the Abyss the very first thing you will want to do is turn in all of your quests and set your Obelisk location here. The obelisk can be found on the second floor of the main building in The Abyss.
Map of the Lower Abyss
You have many different areas available to you for grinding, however my person favorite is at the undead south of our town. You can see my location by where I am on the map. Right where I am standing you can also find two NPC's with quests available to you and even a repeatable one for the undead nearby. This makes the grind... well... seem less of a grind! =D
The quests the two NPC's will give you are as follows:
Disrupting the Guardians
Kill 8 Eternal Swordfighters
Kill 6 Eternal Guards
Kill 3 Eternal Priests
Eerie Undead
Kill Soul Reapers for 5 Trace of Souls. The Soul Reapers can be found all around where the Fallen Warriors can be found. No exact location is needed.
Fallen Warrior
Kill 10 Fallen Warriors. The Fallen Warriors can be found south of the NPC's. They are all over the place so no exact location is needed.
Crystal Blue Persuasion
Collect 
5 Blue Crystal Golem Fragments
Collect 
5 Evolved Golem Fragments
Both golems can be found on the island right above yours closer to town. They are quite spread out so if you want to do the quest it is up to you. Also, the golems can be found on the island with the undead, however their much more rare.
Disrupting the Guardians
Kill 8 Eternal Swordfighters
Kill 6 Eternal Guards
Kill 3 Eternal Priests
After you complete all 4 quests above, you 3 if you decide to skip out on Crystal Blue Persuasion this is the quest you will be grinding for the next level. You have to take a quick flight south of where you get the quest to The Grave of Steel. Here you will need to kill the above listed mobs for the quest. If there are no mobs because everyone is here killing everything you can also follow this path and get a half way decent amount of XP as well
When you ding you will want to head over to the island west of town. Here you will get a new set of quests and also find new mobs, your level to grind. Of course over crowding can happen here as well. If it does, you can find islands all around you (Little ones) that will suffice for grinding.
Of course if it is too crowded over here you can continue with the golems until the next level. You also have another option, which you should do after you get done the quest on this island anyway. That option is to head west onto the island with more Creatures to kill.
Also, for a quick reference I've thrown together a map of The Lower Abyss. It shows the few areas that we can go with a "Threat Level" of that area. Blue means safe, red means dangerous. The threat level is based off the chance Elyos will attack you.
After you reach level 27 your options open up much more. You can continue to grind at this location or you can head to the Upper Abyss and grind in the Upper Abyss. You can also grind at the level 27 - 30 location in the lower abyss. The option is completely up to you and usually it will be made depending on your class.
NOTE: I recommend trying to find a group for the Noschana Training Camp instance before level 30. The mobs in here give quite a bit of XP and you also can't get ganked making it a safe alternative.