One place to start is the local School of Metaphysics, which offers classes on dream interpretation, ghosts and visualization, among other topics.
Or, take a haunted tour of Indianapolis, with tour company Unseen Press. I did the walking tour of central downtown a few months ago, and it was suitably creepy. I'll never think of the Slippery Noodle in the same way again.
Want a less ghostly option? Stop by New Age People at 86th and Ditch for a palm reading, aura photograph or interesting class. You never know what you might unearth here.
If you're looking for a day trip or weekend getaway, head to Camp Chesterfield, "your gateway to the enlightenment of spiritualism." You can take your pick of classes here: runes, numerology, astrology, psychic readings, seances, crystals and everything else you can think of. There's a weekend retreat coming up in a few weeks, and a psychic fair the first Saturday of each month.