I'm sure that you will get greatly varying answers to this one.

I don't see any of the experienced archers answering, so I will throw in my two cents.

I would consider 3" groups good. I assume you are going for hunting, not target shooting.

Like you, I started at about 20 yards and was having no problem with 3" groups (after working out some grip and stance issues). Things get exponentially harder as you get out though. Sometimes (like yesterday), I was struggling with consistent 3" groups at 25 yards. I finished up strong, but had a few erratic flights and down and left misses. My goal is consistent 3" groups at 30 yards for hunting (which I have not reached). I'm only shooting 6" at 30 yards (sometimes better - talking about consistent here).

My thinking is even though the kill zone for deer is obviously bigger than 3", taking a real shot on game from a stand with no warm up shots is more difficult, so I would like some small margin for error.

EDIT: 2 experienced archers beat me to post, so disregard that comment.