There is a lot to do on the Northern Peninsula of Newfoundland, and people often think they can make a day trip up from Gros Morne. Don't do it! There is way too much to do and see, and you need at least one or two nights up at the tip to really experience the best of the area.
The primary attraction (with good reason) is the National Historic Site (and World Heritage Site) of L'Anse aux Meadows. This is the only authenticated Norse settlement in North America, and Parks Canada has done a wonderful job interpreting the story of the discovery of the site, the work of Anne Stine Ingstad and Helge Ingstad in the first archaeological digs, and the further work of Birgitta Wallace at the site. You can wander through the low mounds of the original settlement's building outlines, and visit Norse character interpreters in the reconstructed buildings. Check the site to find out about the special events you can participate in to even better understand the experience of these early settlers.