Are you worried about actual new years celebration? Or just a trip?
Just focusing on the trip and not celebration, Keys are great this time of year. Orange beach and panhandle are great if you like looking out over the water, but could be freezing.
If I wasn't doing that, I'd want to be up in the mountains with snow somewhere. Preferably cabin with snow views and hot tub.
Disney for new years sounds like hell on earth. Would rather leave my kids with their groomer employees than have to be in the parks around christmas or new years. But I'm probably not fun, so maybe if I were being somewhere packed would sound better.