How was I supposed to know the next stop after obtaining the Lord Vessel and defeating the bosses

dark-souls

I had to look up the wiki in order to know that after battling the bosses behind the orange fog gates I had to head for New Londo Ruins and talk with the character up on the roof.

Did I miss something, or was there any way I could have known he would be giving me the Seal Key so that I could continue my quest?

Best Answer

When you placed the lordvessel on the altar, Kingseeker Frampt gave you these instructions:

To achieve your fate, fill the vessel with powerful souls,
commensurate to the great soul of Gwyn.
Scarce few possess such brilliant souls.
Gravelord Nito, the Witch of Izalith,
the Four Kings of New Londo, who inherited the shards of Gwyn's soul...
and Lord Gwyn's former confidant, Seath the Scaleless.
All of their souls are required to satiate the lordvessel.

That's your clue to visit New Londo. From there you could find it just by exploring a little, but there are also some clues in item descriptions that you may or may not have seen on the loading screens, such as the description of the Tin Banishment Catalyst

Catalyst of the banishment sorcerers who
flooded New Londo to seal off away the
Darkwraiths and the Kings who fell to Dark.

This tells you that the kings were sealed away by sorcerers. In-game, this item is found together with the Crimson set which is the same set worn by the sorcerer Ingwald who gives you the key.