New Year beside a harbour is a good one, mostly because of the walk the next morning.
The night
Quayside venues, restaurants and pubs and bars run their own events, and fireworks have featured in some years. Book early: anything with a water view goes months ahead.
The morning after
The harbour shoreline, the beaches and the heath, all empty and bracing. New Year's Day swims take place along this coast; if you join one, read beach safety first and do not go in alone.
Staying
See accommodation, and book well ahead.
Check December events and Christmas in Poole.