CD, I think "Coder" is a noun by itself so "Coder's hangout" should be correct.

Actually, its Coders' Hangout. You're talking about more than one Coder.

There is nothing before the word Coder's, so it's all how you interpret it. Coder's meaning it is a hangout for a coder, or coders' meaning it's all of the coders' hangout. Both are right and both work.

So it would be different if it had the work "The" in front of it? Like "The coders' hangout" ?

"The" would make it plural I believe. "A" would make it singular.

No, the wouldn't make it plural, though a might not make it singular either, depends what it is referring to the coder, or the hangout.

I think it should probably be Coders' due to the fact that there are multiple coders here, unless it is any one of ours in particular .

It could be either...doesn't matter. Putting "the" would work in both instances, too.

Coder's Hangout (one coder's hangout; could still be used if you're just talking about something like a hangout every coder can come to)
Coders' Hangout (referring to more than one coder; also works)

The Coder's Hangout (talking about that one coder's hangout)
The Coders' Hangout (talking about multiple co--you get it by now, though)

So both work. I think.