Puri, home to the Rath Yatra procession and the popular Jagannath Temple, was once famous as one of the best hippy hangouts in the country. Nature lovers also have the option to visit one of the many reserves in the state, places that boast of thousands of species of birds, crocodiles, endangered sea turtles and dolphins. Chilka Lake, a huge saltwater lagoon, is the ideal location for bird lovers. A short distance up the coast lies Konark, one of the most beautiful and traditional medieval-era temples in the country, where the entire surface is covered with intricate sculptures.
Odisha is also famous for its Adivasi population, ancient tribal people who are believed to be descendants of pre-Aryan aboriginal inhabitants. You might not get to meet or interact with them as most are kept hidden from mainstream tourism, but you can certainly become a part of their excellent weekly markets.