Hi asotirhos,
First off, a 680 is a strong score (it's right around the 85th percentile overall), so it could be enough to get you into your first-choice School. As such, a retest might not be necessary. Depending on the Schools that you plan to apply to, you would likely find it beneficial to speak with an Admissions Expert about your overall profile. There's a Forum full of them here:
ask-admission-consultants-124/Since your Quant Scaled Score on Test Day was considerably lower than your practice CAT scores, I'd like to know a bit more about how you took your CATs.
When you took your CATs:
1) Did you take the ENTIRE CAT each time (including the Essay and IR sections)?
2) Did you take them at home?
3) Did you take them at the same time of day as your Official GMAT?
4) Did you ever do ANYTHING during your CATs that you couldn't do on Test Day (pause the CAT, skip sections, take longer breaks, etc.)?
5) Did you ever take a CAT more than once? Had you seen any of the questions before?
GMAT assassins aren't born, they're made,
Rich