What is the accepted procedure for drawing monsters? If I need to draw 8 monsters for 3 gates, it's easy to determine which two will get the extra monster, but do I draw them one by one, looking at them then placing them, or do I draw them all at once and distribute after looking at all 8, or do I blindly distribute them adhering to the agreed upon numbers at each location?
No, you can't look at them - just draw and place.
From the Arkham Horror FAQ, in the Open Gate and Spawn Monster section (on page 2-3), in its discussion of monster surges:
When placing monsters, they must be divided as evenly as possible among the open gates, with no gate having more monsters placed on it than the gate where the monster surge occurred this turn. If there are more monsters to be placed than allowed by the monster limit, the players should decide where monsters will be placed. The players must make this decision before monsters have been drawn from the cup. If the players cannot agree where the monsters are to be placed, the first player decides the placement.
That doesn't explicitly cover the scenario you asked about, but the same principle should apply: you figure out where to put all the monsters you're about to draw, then you draw them.
You definitely do not get to decide where to put a monster once you've looked at it.
That would go against the 'spirit' of the game. Once you've decided the distribution (e.g. 2 at the woods, 1 at the black cave and 1 at The Unnameable), just draw them one by one and place them. I usually do a round robin placement (1 at each gate before putting the others) but it isn't something that is mandated by the rules. Just as long as the end result meets the rule mentioned in Jefromi 's answer.