After the initial dialogue between him and Thongor Silver-Blood, Brother Verulus can be found in the Hall of the Dead or inside Understone Keep.
UESP lists his schedule as follows:
He starts his day in the Understone Keep at 8am, and will wander around the Keep for the entire day, eating at noon and at 6pm, before going to sleep at midnight.
He's essential until you've progressed much longer through the quest The Taste of Death, so he shouldn't be dead.
If you're on PC, you can use
help "Brother Verulus" to find his RefID and then use the command
player.moveto [RefID] (after saving, of course) to teleport to him. The RefID will look something like
0001BB8F, so then you'd type
The quest page lists another solution as well:
Alternately, you can completely ignore Verulus and pick the lock to the hall. Entering the hall this way will trigger the main quest; however, unless you persuade or bribe him, you will not be able to befriend him using the favor quest.
However, depending on your choices later in the quest, you'll have to locate him eventually. If he's dead for some strange reason (you never know with these sandboxy games), you can try the following method posted on reddit to restore him: [PC only] Foolproof guide to resurrecting NPCs.