I've been screwing around in Arena's cities for a while, and I'm still lvl 4. City quests just aren't cutting it, it's really slow.

Everything I've read says you can leave the city and go find randomly generated dungeons, but I haven't found any yet. Do I just keep running in one direction? What do the doorways look like? Will I have to pick their locks? (I'm a warrior.)

I don't want to go on through the MQ until I've levelled up more, but I don't want to keep running errands either. Right now my only option for good XP is to wander around the city at nightfall hoping for random enemies, and that's unreliable.

Have you tried asking bartenders about work? Sometimes they send you to the palace for a job that leads to a non random dungeon. Out in the random terrain around cities dungeon doors look like http://www.gamefaqs.com/pc/564545-the-elder-scrolls-arena/images/screen-18. You can just walk in.

Though if you do need a locked door open as a warrior, just attack a door till you get sent inside the place. In town this can call the guards on you if you don't bash it open quick enough. Just be sure to use a weapon you don't normally use since this damages it. Maybe just some cheap weapon from the equipment shop.

IIRC, most of the randomized dungeons in the game you'll run into will appear as castles/fortresses. If you keep looking around, you'll find some pretty soon. They're smaller than the major dungeons, and tend to have only two floors.

Yay, found my first one! And I just might die in it. Stupid orcs...