Shetland has a wealth of archaeologial sites to explore - Jarlshoff, Old Scatness and Mousa are the jewels in the crown but there are places of interest all over Shetland. Jarlshof is open to the public all year round, be sure to pick up an audio guide to get as much as you can out of your visit. I met up with Shetland Archaeologist, Val Turner to have a quick chat about sites in the isles.
If you want to explore on your own then start by looking at our archaeology page; the Facebook page Archaeology Shetland is a good group to join, especially if you want to join discussions, share photos or ask for tips. You might want to join in a guided tour that takes in archaeology and geology - if you do Shetland Geotours might be what you're looking for.