The Fossil Cliffs Maria Island are perhaps the best place to photograph the sunrise on the island. With a delightfully rocky foreshore and an easterly aspect it is similar to that other great location for sunrises in Tasmania, the Tessellated Pavements on Eaglehawk Neck. The view encompasses the aeons old fossill cliffs, named due to the extraordinary number of ancient fossil shells embedded into the rock, as well as the instantly recognisable Bishop & Clerk.
From your accommodation in the town of Darlington it is close enough to 30 minutes on foot, walking either directly across the island, or around the flat and open northern coast. It is a good idea to check the area out the afternoon prior to a sunrise shoot, just to get an idea regarding potential compositions. It is also a good idea to keep an eye on tide times, as the foreshore (above) would be well under water at high tide.
On your way back after the shoot there are Cape Barren Geese, a couple of old buildings and cemetery, and a very nice stand of blue gums which are well worth stopping at for a look. The more adventurous could also try the ascent of Bishop & Clerk which will take around 2~2.5 hours to the summit, but a fair bit less coming down. There is a very beautiful eucalypt forest on a dolerite boulder field half way up, and the views from the top on a clear day would be stunning (the day I climbed was clouded out). The Tasmanian Parks & Wildlife Service has a very informative walking guide and notes for this area.