Take the ferry from St. Thomas to St. John....when you dock in Cruz Bay, walk around to the left to the National Park Service office/visitor center. You can get a trail map and do some great hiking....with great views....FREE! Of course, you'll want to head to famous Trunk Bay, too.....fee.
Behind the beach at Magen's Bay is a 300 acre preserve co-owned by The Nature Conservancy and the V.I. government. There is a trail that takes you through tropical forest and mangroves in the preserve. It's quite steep at times so if you're going to do the whole trail, get someone to drop you at the top of the trail (off of Magen's Bay Road) and then walk down to the beach. However you can walk part of it on flat ground with access from Magen's Beach. A number of trees are labeled and The Nature Conservancy is currently putting together a brochure for a self guided tour.
To access the trail, go left when entering Magen's at the gate. Drive out to the coconut grove (lots of very tall coconut trees) . Walk through a green open gate and when you come to a T, go left along the trail or right to get to an old arboretum.