The arena is on Biscayne Blvd (aka right on the water) and there are plenty of hotels along the water that will be close to the arena and will also give you the entire South Florida experience with the beach and restaurants, etc. I'd recommend just about any of those hotels especially the Marriott, Holiday Inn and Doubletree. If you're looking to go a little more upscale then the new Epic hotel is supposed to be nice, never stayed there before but haven't heard a bad thing about it.
Now I don't know what kind of events the city might have planned for NYE, which means I don't know if roads will be blocked off, etc which is why I don't recommend you stay in South Miami or Coral Gables because it'd be quite a trek to AAA if everyone is going in one direction. Traffic is already crazy in Miami, and I expect it to be double that with everyone coming into town for these shows plus everyone in town for NYE in general. However if you do want to get away from the crazyness and stay in Coral Gables (where I used to live
) I'd recommend the Biltmore or any hotel that they've recently built near Coconut Grove. The Grove is an awesome place to spend the day before the show if you're not into the beach scene as it has some great shopping and restaurants/bars. Another great area that isn't downtown would be what we call the North Grove. It has some hotels (The Mutiny, Mayfair, Wyndam, Hampton Inn) and great restaurants including my favorite in Miami, Monty's right on the water. It's another one of those that's out of the way a little bit but it'll make for a very pleasant weekend.
To sum up: if you want to stay near the venue and near all the excitement- stay downtown on Biscayne Blvd. If you want to stay away from the venue and see more of Miami (and where the people actually live)-stay in Coral Gables or the Grove. If you all have any other questions feel free to ask me! WOOOO NEW YEARS EVE!!!