Nusa Island is hands down the best place to stay in Kavieng and gets my vote for the best value spot in PNG. There's a good range of accommodation - from shared facilities to executive overwater bungalows. Note that all the facilities have compost toilets which are very eco-friendly.
I stayed in a wonderful overwater bungalow with views to the port (5 mins boat ride to town, 10kina). Great to wake up to the sound of lapping water and birds calling - there is a menagerie of half-tame exotic birds on the island. A highlight, aside from the super friendly owners and staff is the excellent food. The evening buffet is the best deal and most delicious cooking in PNG - be sure to let cook know you want to eat in by mid-afternoon.
Visitors from other hotels are welcome to eat there.More