Head down to the New River near McCoy Falls. It isn't really a waterfall, just a little cat one rapid. You can rent a tube or bring one but it will probably be too cold by then. Just make sure that when you park your car is 100% off the road. New River Junction are river nazis and will tow your car for sure. If you head down a bit farther from there you can even find New River Cave. You find it by finding the PVC pipe sticking out of the hillside with water coming out of it. That is water from the stream that made the cave. There is a fantastic view from the entrance and a waterfall in the back of the cave.

While you stay in/around campus there are a handful of must see and easy sights most of which is a lap around the Drill Field. There is the War Memorial, April 16th Memorial, and the Duck Pond. That all being said the Duck Pond is better during the day and War Memorial I think is best at night. Closer to the Stadium is the Horticultural Garden which is also nice.

While you are in town make sure you stop at TOTS and get a Rail assuming you don't care about your liver. The easiest time would be sometime on Saturday before the game. TOTS tends to get crowded on Friday nights.