Get out and about while you are in Brookings. Start with a visit to the the South Dakota State University.
Of course, limiting yourself to only one place will only ever furnish you with a narrow glimpse into the wider rhythms and life-ways of a region. So set aside a few days to explore Eastern South Dakota's attractions. Madison and Clear Lake are just two of the many other places worth checking out while you're in Eastern South Dakota.
Sioux Falls is 55 miles (89 kilometers) from Brookings. This regional center contains a great selection of things to see, including Washington Pavilion of Arts and Science, Thunder Road Family Fun Park and Augustana College. Sioux Falls Arena, Fawick Park and Falls Park are some of the other interesting sights here that should be on every traveler's itinerary.
If you like to get out into the cold, this area could be the perfect place to go. Grab some gear and go snowboarding and skiing. Head outdoors and get amongst it in the area around Brookings. Try mountain biking or give hiking a go.
Even the best vacation can't go on forever, so when it's time return home, head to the nearest major airport in Watertown, 45 miles (72 kilometers) away.