I have an Ibanez acoustic which mysteriously has a hole/crack/opening in it, on the side directly opposite the soundhole. It's been that way for about a month now, and the hole itself is about two square inches in width.

The guitar originally cost me about $300 - would it be better for me to buy a new one or try to get it repaired? (The sound is getting screwy and I hear it will only get worse)

Get an ovation and it wont happen again

But if you fix it, it would add a bit of character to the guitar. I personally would fix it myself.

It depends. Do you like the guitar in the first place? If you can have it fixed for cheap i don't see any problem. But if a guitar does that mysteriously as you said then i probably would buy a better one.

Personally, I'd buy a new one. I have long lost my trust cheaper equipment, but that's
more because of personal experience.

The lowdown is just this though, guitars shouldn't just produce holes like that. I once
bought a custom Ibanez, and i mistreat the guitar as if it were a Bass. It's been this
way for years, and it never so much as flinched.

Costs for reparation will vary depending on what material the guitar is made of, but it
doesn't sound like it's too expensive. The question is wether it sounds well enough, and
wether or not it will still sound well after the reparation.

I'd buy an Ovation like Pepoke said, but I'm biased, so my voice doesn't really count.