Most quests will have markers, but a few (and some parts of quests) won't have any. That can be an oversight on the part of the developers, or a bug, or because the quest has no specific location. It's not a common thing, by any means, so don't let it turn you off the game.
In the case of "In my Time of Need," I think it's supposed to get you to look around Whiterun for the woman in question.
Spoiler Check the Bannered Mare, the only inn in town.