The question is, what are your goals for your archery? Do you want to hunt? Do you want to compete? Do you want to pick up a new skill? In all cases, the only answer that is appropriate is "as tight as you can." As far as hunting goes, what do you want to hunt? The goal is to get all arrows in the "kill zone" at the maximum distance that you would normally take a shot. If your goal is to take an elk with a bow, then you accuracy goal is significantly looser than if you want to take a squirrel with your bow, but you may be able to get closer to the squirrel (maybe not). For deer hunting, all within a 6" circle is sufficient. Take it down to 3" if you want heart shots, but 6" will get you a repeatable "double lung" shot. Of course, even here the ultimate goal is, as tight as possible.
I shoot a compound with a sight- so it is not really a fair comparison- but I don't shoot multiple arrows at the same bulls-eye when shooting broadheads, because I am tired of refletching my arrows. Even field points are tough on fletchings lately. My goal is to have every arrow shaft touching at least one other arrow shaft at 20 yards. I'm no expert (I've only been shooting for 3 years), and many shoot considerably better than me, I just thought I'd inject a bit of perspective.
Good luck with the long bow, that is a step that I have not taken yet. I guess I am still in training wheels.
One more thing, when you are practicing and your groups start to open up, and they will, stop for the day. Trying to pull them back together will teach you bad form, as at this point you are practicing while fatigued and will develop poor form to compensate for the fatigue. Better to end early and on a good note.