Hello Joan,
I did this last year, the New Years eve dinner was the only time we really "dressed up" so your party frock should be fine as no one went over the top with evening gowns and there was dancing and a live band, even the waiters joined in, then after the meal some of us went to the harbour and watched the fireworks at midnight.
As far as I can remember there was a quiz night in the bar.
Some of the excursions are historical but interesting and there is shopping in Famagusta and Nicosia.
Dave.