I can offer suggestions:
Most of the nicer places in town put together special menus for the evening of the 31st.
The sun goes down earlier here (no daylight savings time) so people tend to eat earlier, you may not be at the restaurant at midnight, because you will have eaten and headed for the festivities already.
Reservations for the spot you pick will be a must, as that week the island is at maximum capacity, so when you find a spot, maybe email them to secure your table.
The whole island is celebrating, rove around or stay in one spot, either way its a blast.
Have fun, tis a wonderful time here!
So, hope that helps, I know you were hoping for suggested restaurants, but I must beg out of that portion, I'm biased.