I feel your pain. There just aren't a lot of worthwhile places to rob in vanilla Oblivion. Mods can help, if you have access to them. One in particular - Vaults of Cyrodiil - adds special treasure-vaults to each of the main cities. Other mods increase the valuables that can be found in the houses of the wealthy or in palaces.
However, something you might consider: rob dungeons.
I know, the game seems built to accommodate killer types, who would descend into caves or ruins, murder the inhabitants, and haul their stuff back to the surface for profit. Playing a murderhobo adventurer is good fun, especially in a cheerful gameworld like Oblivion's, but consider approaching those dungeons like a thief would, by skipping step 2 in my above list: just enter the places, sneak around, and steal what you can - without killing anyone. As Garrett would say, you're a thief, not a murderer!
Not all dungeons would accommodate this approach; some places you need to fight or kill in order to get past the guardians. But the thrill of ghosting through an Ayleid ruin or a fort overrun by big, dumb marauders is a big draw - and robbing some long-forgotten tomb or wizard's hideaway will feel like a really big heist, worthy of a story or two while you and your lowlife friends guzzle some cheap ales in the Bloated Float. 
I'll try out the Vaults of Cyrodiil. Could someone direct me towards mods for places to rob or mods that make stealing more profitable?