My family has gone to DHS twice for NYE. I really enjoy it.
Obviously, MK is the most crowded park on NYE. It gets incredibly congested and hard to move around. Think of MK as the "Times Square" of Disney World.
EPCOT gets just as crowded. Because it's larger than MK, it seems to absorb the crowds much better. There's parties throughout the World Showcase. There are floods of people, but the CM's seem to keep people moving.
Animal Kingdom is closed at night, leaving DHS as the last choice. DHS is the least crowded of the three parks. We have entered DHS as late as ~9pm and never had a problem getting in.
Having a reservation works in your favor. Even if you're staying offsite, I BELIEVE you can enter the park up to a Phase 3 closure.
DHS is a lot more family friendly. For one, it's easier to move around. I feel like EPCOT is more of a big adult rave-type party. There's DJs, there's drinking, it gets pretty crazy over there. At DHS, though, people seem to do their own thing until around 10-10:30pm. Some people dance in front of the hat - as there's a band and DJ playing throughout the night.. but for the most part, it just feels like a very crowded night at the park.
Seeing as you have a dinner reservation, be on the lookout for noisemakers and hats. CMs will be hanging them out throughout the night - but they usually run out by 8 or 9pm.
THe best spot to watch the fireworks, as a PP said, is right in front of the hat. But it could be congested and there's not many spots to sit. You could grab a seat in front of Prime Time Cafe. It's slightly obstructed, but it has seats and there's a temporary pop-up bar right there. Grab an electric lemonade and countdown to the New Year. I'd recommend getting there around 11pm and saving a seat. Don't get up. If you need a drink or food, send a runner and save their spot. People are like vultures looking for a seat. They'll snatch it right up and won't think twice about joining your family.
For more info, read my book - there's an entire chapter on NYE at Disney: survivedisxmas.com
Join in on the Christmas DIScussion this Saturday, Nov. 1st at 12pm EST!