One of your first stops should be Cocos Islands Visitor Centre. Here, you'll be able to find your bearings and get some great ideas before you set out exploring.
You'll soon find out why this West Island tourist information center is a hit with travelers. If you're looking for more to do and see here, Trannies Beach, and Kite Beach are in this area as well. They won't take long to reach from Cocos Keeling Islands Visitor Centre.