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. 🙃

Morrowind already has map markers. They're used for MOST quests. There are only a handful that give directions based on landmarks without also marking the objective location. And only one of which I can recall where the directions given are wrong. It does not, however, allow fast traveling between marked points.

I would always "fast travel" to a new spot by orienting myself toward the part of the map the NPC marked and then using a spell to buff my acrobatics skill by 1000 (like the scrolls of Icarian flight found outside Seyda Neen) and just jump there.