One of our favorite places to go hiking is Dupont State Forest about 40 minutes from the Chalet: http://www.dupontforest.com. The park is known for its spectacular waterfalls.
Most visitors hike the three mile roundtrip to see Hooker, Triple and High Falls. If you are up for a longer hike or maybe you have bikes with you, bring a picnic lunch to enjoy at one of the beautiful lakes at the park. Bridal Veil Falls is also spectacular, you can actually walk behind the waterfall!