"Scrutinize" doesn't mean the same thing as "stare". To scrutinize means to examine something with great analytical attention to detail. To stare means simply to look at something fixedly. You scrutinize a crime scene, looking all over for evidence. You stare at a streaker, but probably don't scrutinize him.
And none of the words suggested by Mystery1 are exactly synonymous with "stare" either. Nor does "glare", which implies anger or disapproval associated with the looking.
Why are you trying to avoid "stare"? It's a perfectly good, simple, and well-understood verb.
