I don’t know about New Vegas, but the trick with Morrowind is that when the guy tells you, you need to go to a cave west of town, that you then get lost, run into a naked barbarian and help get his clothes back, then you run into a lady who got robbed, but fell in love with the robber, so you help reunite them, and then you’re halfway across the map and have long forgotten that you were supposed to find a cave, but you had a much better time than you could have had in that cave.
Also, the cave might be south of town. It happens. 🙃