ToME: the Tales of Maj'Eyal

So at the start of the game, I traveled a few screens over and killed the big gnarly bear. My quest log says that part is completed, but I need to find the heart of the evil or some such. I'm not sure what to do now

You need to head back to the world map (you might want to 'u'se your Orb of scrying and see what the Bear dropped).
From there you'll be able to find your next dungeon (Heart of the Gloom, I expect).

It's in a different dungeon, to the east ("The Heart of the Gloom"). Use the rod of recall to escape to the world map and head on over.