Once you're both high level and well geared, generally doing what you feel the most comfortable with will provide the fastest AP, there are no diminishing returns on AP gain so the speed at which you level up should be pretty consistent once you've found your preferred method of grinding. More importantly is just really finding the content you're happiest with farming out of the content available in game.
There is also a one week AP boost that is available from The Secret World store that will provide you double AP for the week it is active, which can prove quite significant if you're going for a bit of a short term grind.
Nightmare marked mobs
Once you get to Transylvania a lot of the mobs will be nightmare mobs - mobs with lots of health performing lots of damage while having a weakness that you can optimise your build against to get them down quickly. These mobs will also provide a lot more experience than normal mobs to focusing on killing a bunch of these during your farming session will result in quite a few more AP than if you focussed on lower level/normal mobs.
Your ability to take down nightmare mobs solo will depend quite heavily on your gear and skill setup, if you can't take them down solo you can try grouping up or one of the other options below.
Re-clearing old regions
Savage Coast (excluding Blue Mountain) and Transylvania are good because they have a lot of quests close together but really any region you find you can run through quickly will work. This works especially well if you're running solo since you're not relying on anybody other than yourself, and even more so once you're familiar with the quest start/quest ending location so you can run through the quests as efficiently as possible.
This can provide a lot of variety as you can re-complete each of the missions every few days or so you can effectively move from area to area picking out the parts of the story that are packed together in each region.
Repeatedly running through instances
This works especially well with instances that can be cleared quickly (like Anhk) but it is going to be at least partially down to the quality of your party how fast you can run through them. If you're carrying players who're not familiar with the instance in question this is only going to slow you down.
Spamming PvP and taking part in the objectives on the winning side (last time I played properly the winning side was frequently the Illuminati) will result in a pretty consistent stream of AP/SP and marks. If you're not on the winning side though it's normally more efficient to go with one of the other methods.