Hi Natalie!
I do have to say that I think Port Orleans French Quarter is the most romantic of the moderate resorts BUT, since you live in New Orleans, perhaps Caribbean Beach would be more like a "vacation" to you!
Caribbean Beach is themed like, well, the Caribbean! Different sections of the resort are decorated as different locales of the Caribbean. The pool is top notch. Strolling hand in hand along the sandy beaches or sharing a hammock along the shores will be quite romantic!
A trade off of Caribbean Beach is that it is a much larger resort, but if you don't have any little ones in tow, you may not mind!
Also, if you can swing it, an upgrade to either Animal Kingdom Lodge or Wilderness Lodge would be tops for romance in my book. Keep an eye on the
Special Offers page, and see if maybe a discount would put these in your price range. If so, it might just be worth the splurge!