So I'll throw out my own two cents on this one.
Nito to me seems to want nothing more than to rest as the Dead should. As you see when you join the Gravelords he simply sits unmoving in his coffin accepting eyes of death from his followers. Also unlike most covenants Nito actually has one of his skeletons bring you to him as opposed to using his own power.
If I were to guess as to Nito's allegiance in the game I would say that he is against both the Age of Fire and also against The Age of Man. Why? I suggest this is because of the way his covenant works.
Nito goes out and sends his minions to curse the worlds of other undead making it harder to progress through levels. From this I would suggest that he is trying in his own way to hinder players from even getting to the end of the game. Now I'm not one hundred percent sure if a cursed person has to be human or not but if they are I would think that Nito uses the curse to force them to come to you where the Gravelord servant kills them scattering/ allowing Nito to collect the humanity.
Why I think he is against the age of fire it mentions in the opening sequence "with fire came disparity" and as Nito seemingly just wants to be left alone to be dead it can be considered that where disparity is present action is needed by him to subdue it.
As for the Age of Man if everything became like New Londo and ghosts roamed the earth and humanity was constantly warred over, again, Nito would be put in the position of having to be vigilant so people did not try to kill him to steal his power. In my opinion the only reason he attacks you is because he hasn't summoned you and fears you will steal his soul. As to what a dead person who wants to pretend he is dead wants with a Lord Soul I don't know.
Now with the speculation. Nito's overall goal as I see it is to create the Age of the Dead, perhaps if a normal undead is cursed and killed it becomes dead and can't use its Dark Sign, and during that time where everyone is dead and trying to be dead Nito has no fear of human/things wanting his power. In this way his goal would be to end disparity by both ending the first flame as well as destroying the threat that the DarkWraiths pose to him.
Throw down your own ideas here i have some work to do refining this idea/ arguement for the Age of the Dead (my own personal wish for a new ending to DS) and perhaps maybe understanding a really obscure, albiet popular, character.