We caught the bus from Busan and the trip was about 2 1/2 hours to the main bus terminal on the island and then another 45 minutes to where we were staying. The island is essentially the top of a mountain so most of the roads and settlements hug the coastline making getting anywhere on the island a bit of a trek. Buses are certainly the cheapest way to get around costing between 1,300 won and 2,900 won depending on where and how far you are traveling. If you get motion sickness bring some pills because the roads are windy as hell but make sure you keep that camera handy as well because the views are spectacular. The buses were also the trickiest part of our whole stay. Some of them don't come very regularly so be prepared to sit around for 30 - 40 minutes.
The sites we focused on for our trip included the rice terraces at Daraengi village (where we stayed), Boriam temple, Sangju beach and the German village. All of them were great but if I were to cut one out it would have to be the German village. It isn't exactly German and all of the "German" food was really expensive. Personally I think the best part of Namhae is the scenery, so my suggestion would be to focus on the natural sites rather than the tourist traps like the German village if you find yourself pressed for time.
I may write another post with more details on each site we visited, our favorite coffee shop etc if that is something you guys would be interested in. For now I just want to share some pictures!
Sunrise at Daraengi village
Rice terrace of Daraengi village
View from the top of Boriam temple
Let me know if you guys would like more details on getting to and around Namhae!