How do I wire Neutral on a AC disconnect box?
Read the instructions that come with the box.
I've looked at multiple AC disconnect boxes, though haven't ordered any yet.
On every one I've seen so far, they have a connection for both phases of the 220v, and also a connection that appears to be for Ground.
Where do I connect Neutral?
You probably don't. Cap it off.
What did you attach it to in the electric panel???
I'm bringing 10-3wG into the quick-disconnect
All outdoor A/Cs I'm familiar with simply take 2 hots and a ground; 10/2 would have sufficed.
and haven't yet purchased the air conditioner itself. Do air conditioners even use Neutral?
Bingo, pick out your A/C and then do your electrical per the unit's instructions.
Do I just tie the two Neutral together with a wirenut, akin to a regular lightswitch?
The A/C won't have one so just cap off the extra wire inside the disconnect box.
I think you're getting confused with electric dryers and stoves which usually need 120v for the electronics; the heating elements are 240v.
Picture added per comments:
A 240v appliance with 120v electronics will require a plug like this and the appliance internals will be wired to take the power source they require.