There are many places to visit in Bhubaneswar-Temple city. You can go temple hopping in the old town area, the famous ones are Lingaraj temple, Raja Rani temple, but there are many more. You can visit Jayadeva vatika if you want to.visit a park. You can also visit the museum and planetarium.
Bhubaneswar as the city is quite filled up with temples which can be visited if you want to, however if you want to see some unexplored places around then you will have to go outside the city. Some of them are-
Lalitgiri- ruins of buddhist monastery
Ratnagiri- ruins of buddhist monastery
JIrang Monastery
Dabarkhol waterfall
Deodhar Waterfall
Sapua Dam
Sattkosi Tiger Reserve