There are only about 35 Dungeons that are tied to quests, some have items, some you just have to show up to trigger the quest
http://www.uesp.net/wiki/Skyrim:Dungeon_Quests
Most quest items will not leave your inventory until you have done the quest. Some won't ever leave, quest items have no weight penalty. So, if you pick up a quest item, it will stay with you. Most quest items have a unique name, so that helps.
Now, the game will randomly assign a dungeon for the Radiant Quests that are offered. So, make sure you save before asking for any of those, in case you don't' want to go to a particular place.