Both of the following restaurants as well as the local mac nut farm are owned and operated by the Purdy family. You'll be warmly welcomed at any of their establishments.
Kamuela's Bar and Grill is in central Kaunakakai, open for breakfast, lunch, and dinner, daily. They offer local & mainland dishes at reasonable prices.
Kamuela's Cookhouse in Kualapuu used to be the Sugar Mill cafeteria. It is the best restaurant in Kualapuu ...well, it's the only restaurant here, but it still lives up to its billing of being "purdy" good. Breakfast and Lunch only.
We ate our first dinner on Molokai at the Kaunakakai location. I ordered the grilled Mahi Mahi and my husband the lemon chicken. While I enjoyed my fish, the next time we came back, we both ordered the lemon chicken (much more flavor than the usual bland dish that gets served in most Chinese restaurants.)
Their portions are large, and if you Kamuela-size it for $2 extra, you get even more. Don't forget to end your meal with a slice of their homemade chocolate macnut pie, especially if you like pecan pie.
The Purdy's harvest and sell roasted Mac nuts (without any oils, preservatives or pestisides, and damn tasty), and their farm is well worth a visit!