I agree with Rico. Searching can be performed from an adjacent space, so that part is definitely valid. Doing things with quest objectives is usually outlined int he particular quest, so it may vary, but unless the quest rules say that you must be on top of the objective marker (not adjacent), then you're golden.
This doesn't mean that it's pointless to post guards, mind you. Even if a hero moves in, searches and moves out again (interrupting his move action to search or perhaps using fatigue to move), he probably won't get too far away after searching, so whatever guard monster was there can follow him and attack. I'm pretty sure the OL also has a couple of cards that let him spontaneously attack with a monster when a hero moves too close (I don't have the OL deck memorized or anything, but that seems familiar to me.)