APs can get in to any park and parking lot up to a Phase 3 closure, which is recently the highest closure level. Phase 4 means nobody in that isn't already in, but that hasn't happened in a few years.
That said, even just later in the day, people will already be staking out spots for fireworks, lines will be out of control and you will pretty much be limited to whatever you have FP+ for (if you can make any). I would make sure you have an ADR for dinner, or be prepared to wait in insane lines for CS.
We've done NYE at EPCOT recently and I vastly prefer it to NYE at Magic Kingdom (we did Magic Kingdom in 2012, which ended up being a Phase 3 closure and ... never again). The fireworks are better, there are DJs and dance parties in various countries around the WS and it just feels more "New Year's Eve" to me, like shooting off small fireworks as WS countries hit Midnight. Honestly, I would put it up there with celebrating NYE in Times Square as far as "experience" goes. We don't have kiddos, though, so there's that to consider.
Good luck! NYE is fun, but definitely not for the faint of heart! Be prepared for a lot of standing around and waiting, packed amongst LOTS of people.